Manin, Panchishkin — *Introduction to Modern Number Theory* (Fast Track 3.34) — Audit + Gap Plan

Book: Yuri I. Manin, Alexei A. Panchishkin, Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories (Springer Encyclopaedia of Mathematical Sciences, Vol. 49 — Number Theory I; 2nd ed. 2005, xv + 514 pp.). Originally published 1995; the 2nd edition substantially extends the coverage of Galois representations, $p$-adic $L$-functions, Iwasawa theory, and the post-Wiles arithmetic of modular forms.

Fast Track entry: 3.34. Listed in docs/catalogs/FASTTRACK_BOOKLIST.md as "Number theory, algebraic geometry — BUY".

Purpose of this plan: lightweight audit-and-gap pass (P1-lite + P2

• P3-lite of the orchestration protocol). Output is a concrete punch-list of new units so that Introduction to Modern Number Theory (IMNT hereafter) is covered to the equivalence threshold (≥95%; see docs/plans/FASTTRACK_EQUIVALENCE_PLAN.md §3.4). Mirrors the Brown-Higgins-Sivera NAT plan in structure. Not a full P1 audit; IMNT is a 514-page encyclopaedic survey densely cross-referenced across six chapters and three parts, and a line-level inventory is a multi-week pass. This plan works from IMNT's part-and-chapter structure and the authors' distinctive editorial choices, produces the gap punch-list, and stops there.

Sourcing status: REDUCED. No local PDF in reference/textbooks-extra/, reference/fasttrack-texts/, or reference/book-collection/free-downloads/. The Springer page requires authentication; this plan was produced from canonical knowledge of IMNT's structure (the part/chapter/section outline of Number Theory I in the Encyclopaedia of Mathematical Sciences is public and stable across editions) cross-referenced against the peer sources in §1. A full P1 inventory at theorem-level granularity is deferred until a copy is sourced (target: paid Springer download or Anna's Archive). The §3 punch-list is robust to this gap because IMNT's content map is fixed by its three parts (Problems and Techniques / Ideas and Theories / Analogies and Visions) and the sub-disciplines they cover; the line-number-anchored anchor list in §4 is the part that genuinely needs the PDF.

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§1 What IMNT is for

IMNT is the encyclopaedic survey of modern arithmetic geometry by one of its founders. Where Silverman's Arithmetic of Elliptic Curves gives a focused graduate textbook on a single arithmetic object, and Neukirch's Algebraic Number Theory develops the classical theory of number fields in textbook form, Manin-Panchishkin takes the bird's-eye view: zeta functions, $L$-functions, modular forms, Galois representations, $p$-adic methods, Iwasawa theory, étale cohomology, and the post-1995 Wiles / modularity landscape are presented as a single connected programme, with proofs sketched and references to the technical literature rather than fully worked out.

Distinctive contributions, in the order IMNT develops them:

1. Problems-first framing. Part I ("Problems and Techniques") opens with Diophantine equations, the absolute Galois group $\mathrm{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$, and the classical problem of representing integers by quadratic forms — then the technical machinery is motivated by these problems. This is the opposite of the textbook order (technique first, problems as exercises).
2. Arithmetic of algebraic numbers as a single chapter. Number fields, rings of integers, units, ideal class groups, $L$-functions of number fields, Chebotarev density — Neukirch covers each in a full chapter; IMNT compresses to one because the audience already knows the textbook story.
3. Zeta and $L$-functions as the spine. Chapter 6 of Part II organises the entire subject around $L$-functions: Riemann zeta, Dirichlet $L$, Dedekind zeta, Hecke $L$, Artin $L$, automorphic $L$, $L$-functions of modular forms, $L$-functions of elliptic curves, and (in the 2nd ed.) $p$-adic $L$-functions. The functional equation, analytic continuation, and special values (Euler 1735, class number formula, Birch-Swinnerton-Dyer, Tate twist conjectures) appear as instances of one structural pattern.
4. Modular forms and the Eichler-Shimura programme. Modular forms, Hecke operators, Hecke algebras, the Eichler-Shimura correspondence between weight-2 cusp forms and $\ell$-adic Galois representations attached to modular curves. The bridge from modular forms to Galois representations, with the Eichler-Shimura congruence relation as the central technical bridge.
5. Galois representations. $\ell$-adic representations of $\mathrm{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$, Tate modules of elliptic curves, the étale cohomology of modular curves, the Langlands philosophy "automorphic forms ↔ Galois representations" in survey form.
6. Iwasawa theory. ${\mathbb{Z}}_p$-extensions, Iwasawa $\lambda ,\mu$-invariants, the Main Conjecture (Mazur-Wiles), and $p$-adic $L$-functions as a parallel analytic object alongside complex $L$-functions.
7. Post-Wiles synthesis (2nd ed.). Substantial new material in the 2nd ed. on the modularity theorem (Wiles 1995, Breuil-Conrad-Diamond-Taylor 2001), the BSD conjecture, the Sato-Tate conjecture, and the Langlands programme as the unifying frame.
8. Analogies with function fields and arithmetic surfaces. Part III ("Analogies and Visions") draws the curve-over-${\mathbb{F}}_q$ ↔ number-field analogy explicit: Weil conjectures (Deligne 1974), arithmetic surfaces (Arakelov, Faltings 1984), zeta functions of schemes over $\mathbb{Z}$. This is the encyclopaedic synthesis that justifies the title's word "modern".

IMNT is not a first introduction to number theory. It assumes Serre A Course in Arithmetic (3.14) or equivalent for the elementary background, basic algebraic number theory (Neukirch chapters 1–3 level), basic algebraic geometry (varieties + schemes at Hartshorne Ch. I–II level), and basic Galois theory. It is the canonical survey entry point to modern arithmetic geometry — the book one reads to see the whole landscape before committing to Silverman / Diamond-Shurman / Neukirch / Bombieri-Gubler for the technical depth.

Peer sources (in addition to the IMNT book itself; ≥3 required per the audit protocol):

• J. H. Silverman, The Arithmetic of Elliptic Curves (Springer GTM 106, 2nd ed. 2009) — the canonical textbook on elliptic curves over number fields, $\ell$-adic representations of $E$, the Mordell-Weil and Mazur torsion theorems.
• F. Diamond, J. Shurman, A First Course in Modular Forms (Springer GTM 228, 2005) — the canonical textbook on modular forms, Hecke algebras, the Eichler-Shimura relation, and modular Galois representations at graduate-textbook depth.
• J. Neukirch, Algebraic Number Theory (Springer Grundlehren 322,
  1999. — the canonical textbook on number fields, ideal class groups, local-global duality, $\zeta$ and $L$-functions of number fields, class field theory.
• E. Bombieri, W. Gubler, Heights in Diophantine Geometry (Cambridge New Mathematical Monographs 4, 2006) — the canonical reference for heights, Mordell-Weil, the Mordell / Faltings theorem, and the arithmetic of abelian varieties at the level IMNT surveys.
• (Supplementary) J. P. Serre, A Course in Arithmetic (Springer GTM 7, 1973) — the elementary number-theory anchor, FT entry 3.14, which IMNT explicitly assumes.

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§2 Coverage table (Codex vs IMNT)

Cross-referenced against the current Codex corpus (content/00-precalc/ through content/20-philosophy/). ✓ = covered, △ = partial / different framing, ✗ = not covered.

IMNT topic	Codex unit(s)	Status	Note
Diophantine equations (Pell, Mordell, Fermat-Catalan, ABC)	—	✗	Gap. No Diophantine equations chapter.
Number fields, ring of integers, ideal class group	—	✗	Gap. Algebraic number theory absent.
Local fields, $p$-adic numbers ${\mathbb{Q}}_p$	△	△	Touched in passing in 02-analysis/ Ostrowski-adjacent material; no dedicated unit.
Adeles and ideles	—	✗	Gap.
Class field theory (statements)	—	✗	Gap.
Riemann zeta function $\zeta (s)$ — functional eq, analytic continuation	—	✗	Gap. Riemann 1859 originator-citation expected.
Dirichlet $L$-functions	—	✗	Gap. Dirichlet 1837 originator.
Dedekind zeta, Hecke $L$, Artin $L$	—	✗	Gap.
Elliptic curves (algebraic-geometry side)	✓	✓	04.04.03-elliptic-curves.md covers Mordell-Weil / Weierstrass form / group law.
Elliptic curves over $\mathbb{Q}$ — arithmetic side (heights, $E(\mathbb{Q})$ structure, $L$-function $L(E,s)$)	△	△	Algebraic-geometric side present (04.04.03); arithmetic-side units (BSD, $L$-function, Selmer / Tate-Shafarevich) absent.
Modular group ${\mathrm{SL}}_2(\mathbb{Z})$, action on $\mathbb{H}$	✓	✓	Present in 06.01.08-mobius-transformations.md as a pointer.
Modular forms (definition, Eisenstein series, cusp forms, weight, level)	△	△	Referenced in 06.08.02-vhs-jacobian.md synthesis ("Eisenstein series $E_4,E_6$ generating the ring of modular forms") but no dedicated unit.
Hecke operators, Hecke algebra, eigenforms	—	✗	Gap. Hecke 1936-37 originator.
Eichler-Shimura congruence relation	—	✗	Gap. Eichler 1954, Shimura 1957 originators.
$\ell$-adic Galois representations	—	✗	Gap.
Tate module $T_{\ell }E$ of an elliptic curve	—	✗	Gap.
Modular Galois representation attached to a cusp form	—	✗	Gap.
Modularity theorem (statement)	—	✗	Gap. Wiles 1995, BCDT 2001.
BSD conjecture (statement)	—	✗	Gap.
${\mathbb{Z}}_p$-extensions, Iwasawa $\lambda ,\mu$-invariants	—	✗	Gap. Iwasawa 1959 originator.
$p$-adic $L$-functions, Main Conjecture (Mazur-Wiles)	—	✗	Gap.
Weil conjectures (statement, Deligne proof sketch)	△	△	Riemann-Hypothesis-for-varieties mentioned in 04.03/ cohomology-of-projective survey but no dedicated unit. Deligne 1974 originator.
Étale cohomology (survey)	—	✗	Gap. Strict prerequisite for the Galois-representation unit.
Arakelov geometry, arithmetic surfaces, Faltings	—	✗	Gap (low priority — Master-tier survey only).
Sato-Tate conjecture (statement)	—	✗	Gap (low priority — Master pointer).
Langlands programme (survey pointer)	—	✗	Gap (low priority — non-goal per §5).
ABC conjecture, Faltings / Mordell theorem (statements)	—	✗	Gap (low priority — Master pointer).

Aggregate coverage estimate: ~5% of IMNT has corresponding Codex units (only the elliptic-curves-as-algebraic-curves unit 04.04.03 and the modular-group / Möbius-transformations pointer in 06.01.08). The gap is essentially total. This is unsurprising — the Codex has no number-theory chapter; arithmetic geometry has appeared only where it intersects with the algebraic-geometry curriculum (Mordell-Weil for elliptic curves, modular group via hyperbolic geometry, period mappings via VHS).

Structural recommendation. A new chapter is required. Two options:

• Option A (preferred): 21-number-theory/ as a new top-level chapter parallel to 04-algebraic-geometry/ and 06-riemann-surfaces/. Number theory is its own discipline with its own foundational sequencing (number fields → zeta/L → modular forms → Galois representations → Iwasawa), and folding it into 04-algebraic-geometry/ distorts both. This matches the FT booklist's treatment of 3.14 (Serre Cours d'arithmétique) and 3.34 (Manin-Panchishkin) as a distinct strand.
• Option B (alternative): 04.12-number-theory/ as a sub-chapter of algebraic geometry. Cheaper to set up (no new chapter scaffolding), but mis-classifies number theory as a subset of algebraic geometry, which is the modern arithmetic-geometry view but not how the Codex sequences other classical disciplines (real analysis is not a sub-chapter of measure theory, etc.).

Strong recommendation: Option A. Create content/21-number-theory/ with sub-folders for the priority-1 units below. The chapter sits naturally between 20-philosophy/ and any future physics deepenings; its dependency edges go into 04-algebraic-geometry/ (for schemes / elliptic curves) and out to 06-riemann-surfaces/ (for modular forms as automorphic forms on $\mathbb{H}/\Gamma$).

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§3 Gap punch-list (P3-lite — units to write, priority-ordered)

Priority 0 — strict prerequisites:

• Algebraic number theory primer. Neukirch Ch. 1–3 equivalent — number fields, ring of integers, ideal class group, units. Currently absent from the Codex; required before any IMNT unit can be written. Tentative unit 21.01.01 through 21.01.05.
• Local fields / $p$-adic numbers. ${\mathbb{Q}}_p$ as completion, Hensel's lemma, ramification, local-global. Tentative 21.02.01 through 21.02.04. May overlap with 02-analysis/ Ostrowski material; consolidate.
• Étale cohomology survey (pointer-only OK at this stage). Needed for any honest Galois-representation unit. Could live as 04.12.xx inside the AG chapter rather than the new NT chapter.

Priority 1 — high-leverage, captures IMNT's central content:

1. 21.03.01 Riemann zeta function $\zeta (s)$. Definition, Euler product, functional equation, analytic continuation, the Riemann hypothesis (statement only). Riemann 1859 originator-citation. Three-tier; Beginner = Euler product + $\zeta (2)={\pi }^2/6$; Intermediate = functional equation via theta-function symmetry; Master = the full Riemann 1859 derivation. ~2000 words.
2. 21.03.02 Dirichlet $L$-functions $L(s,\chi )$. Dirichlet characters, $L(s,\chi )$, non-vanishing at $s=1$, Dirichlet's theorem on primes in arithmetic progressions. Dirichlet 1837 originator. Three-tier. ~1800 words.
3. 21.03.03 Dedekind zeta function, Hecke $L$, Artin $L$. Survey unit: ${\zeta }_K(s)$ of a number field, Hecke characters, Artin $L$-functions attached to Galois representations, the functional equation in each case. Master tier required; Beginner = Dedekind only. ~2000 words.
4. 21.04.01 Modular forms on ${\mathrm{SL}}_2(\mathbb{Z})$. Definition, weight, holomorphy at infinity, Eisenstein series $E_k$, cusp forms, dimension formula for $M_k$. Diamond-Shurman Ch. 1 anchor; IMNT Ch. 6 anchor. Three-tier. ~2200 words. Foundational for the rest of the modular-forms units.
5. 21.04.02 Hecke operators and Hecke algebra. $T_p$ acting on $M_k(\Gamma )$, multiplicativity, eigenforms, the Hecke algebra $\mathbb{T}$. Hecke 1936-37 Math. Ann. originator-citation; Diamond-Shurman Ch. 5 anchor. Three-tier. ~2000 words.
6. 21.04.03 Eichler-Shimura correspondence. Statement: weight-2 cusp eigenforms ↔ 2-dimensional $\ell$-adic Galois representations on the Tate module of the Jacobian of $X_0(N)$. Eichler 1954 + Shimura 1957 originator-citation. Master-tier; Intermediate covers the statement and the $X_0(N)$ side; Beginner is a pointer only. ~2500 words.
7. 21.05.01 $\ell$-adic Galois representations. Definition, continuity, ramification, examples (Tate module of an elliptic curve $T_{\ell }E$, modular Galois representation ${\rho }_f$). Master-tier-heavy; depends on Priority-0 étale cohomology pointer. ~2500 words.
8. 21.06.01 Modularity theorem (statement) and BSD. Statement of the modularity theorem (Wiles 1995 Ann. Math. 141; BCDT 2001 J. AMS 14 for the full statement); statement of the BSD conjecture; the bridge $L(E,s)=L(f_E,s)$. Master-tier; Beginner = "every elliptic curve over $\mathbb{Q}$ is modular". ~2200 words. No proof — defer to non-goals (§5).

Priority 2 — Iwasawa, $p$-adic methods, Weil conjectures:

9. 21.07.01 ${\mathbb{Z}}_p$-extensions and Iwasawa theory. ${\mathbb{Z}}_p$-extension of a number field, Iwasawa's $\lambda$ and $\mu$ invariants, the Iwasawa algebra $\Lambda$. Iwasawa 1959 Bull. AMS originator. ~2000 words. Master-tier-heavy.
10. 21.07.02 $p$-adic $L$-functions and Main Conjecture. Kubota-Leopoldt $p$-adic $L$-function, the Mazur-Wiles Main Conjecture (statement). Master-tier survey unit. ~1800 words.
11. 21.08.01 Weil conjectures (statement and Deligne proof sketch). Statement: rationality, functional equation, Riemann hypothesis, Betti numbers, for $\zeta$-functions of smooth projective varieties over ${\mathbb{F}}_q$. Deligne 1974 Publ. Math. IHES 43 originator-citation for the RH. Could sit in 04-algebraic-geometry/ instead of 21-number-theory/ given the overlap; cross-link. ~2200 words.

Priority 3 — survey deepenings (Master-tier, optional for FT equivalence):

12. 21.06.02 Sato-Tate conjecture. Statement, proof (Taylor et al. 2008-2011); pointer only. ~1200 words.
13. 21.09.01 Arakelov geometry / arithmetic surfaces (survey). Faltings 1984 Ann. Math. originator; Bombieri-Gubler anchor. Master-only pointer. ~1500 words.
14. 21.09.02 Faltings / Mordell theorem. Statement; pointer unit. ~1200 words.

Priority 4 — pointers to the Langlands programme (deferred per §5):

15. 21.10.01 Langlands philosophy survey. Statement-level only; defer technical content. ~1000 words.

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§4 Implementation sketch (P3 → P4)

For a full IMNT coverage pass, items 1–8 are the minimum set to hit the FT equivalence threshold, with the Priority-0 prerequisites (number fields, local fields, étale cohomology pointer) shipped first. Realistic production estimate (mirroring Hartshorne / Lawson-Michelsohn / Brown 1.05 batches):

• ~3.5–4.5 hours per unit. IMNT units skew higher than the corpus average because the master tier requires careful $L$-function and Galois-representation notation, multiple originator citations per unit, and tight integration with the algebraic-geometry chapter.
• 8 priority-1 units × ~4 hours = ~32 hours of focused production for the high-leverage core.
• Plus 3 Priority-0 prereq units × ~3 hours = ~9 hours.
• Plus 3 priority-2 units × ~3.5 hours = ~11 hours.
• Total ~52 hours to reach ≥90% IMNT equivalence; ~60 hours with priority-3 to hit ≥95%. Fits a focused 7–10 day window.

Originator-prose target. Several IMNT units are originator-eligible per docs/plans/FASTTRACK_EQUIVALENCE_PLAN.md §10:

• Riemann 1859, "Über die Anzahl der Primzahlen unter einer gegebenen Größe," Monatsber. Berliner Akad. — the zeta-function paper. Originator citation for 21.03.01.
• Dirichlet 1837, "Beweis des Satzes, dass jede unbegrenzte arithmetische Progression …," Abhandl. Königl. Preuss. Akad. — Dirichlet $L$-functions and the arithmetic-progressions theorem. Originator citation for 21.03.02.
• Hecke 1936, "Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung," Math. Ann. 112; Hecke 1937, "Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung. I, II," Math. Ann. 114. Hecke operators, Hecke algebra. Originator citation for 21.04.02.
• Eichler 1954, "Quaternäre quadratische Formen und die Riemannsche Vermutung für die Kongruenzzetafunktion," Arch. Math. 5; Shimura 1957, "Correspondances modulaires et les fonctions $\zeta$ de courbes algébriques," J. Math. Soc. Japan
  10. The Eichler-Shimura correspondence. Originator citation for 21.04.03.
• Iwasawa 1959, "On $\Gamma$-extensions of algebraic number fields," Bull. AMS 65. Originator citation for 21.07.01.
• Deligne 1974, "La conjecture de Weil. I," Publ. Math. IHES
  43. The Riemann Hypothesis for varieties over ${\mathbb{F}}_q$. Originator citation for 21.08.01.
• Wiles 1995, "Modular elliptic curves and Fermat's last theorem," Ann. Math. 141. Modularity for semistable elliptic curves; with Breuil-Conrad-Diamond-Taylor 2001, J. AMS 14, full modularity. Originator-citation set for 21.06.01.

Notation crosswalk. IMNT follows Bourbaki / French-school conventions:

• ${\mathbb{Q}}_p$ for the $p$-adic completion; ${\mathbb{Z}}_p$ for the $p$-adic integers; ${\mathbb{C}}_p$ for the completion of $\overline{{\mathbb{Q}}_p}$.
• $G_K:=\mathrm{Gal}(\overline{K}/K)$ for the absolute Galois group; $G_{\mathbb{Q}}$ for the rationals.
• $\zeta (s)$, $L(s,\chi )$, ${\zeta }_K(s)$, $L(s,\pi )$ for the successive $L$-function generalisations; consistent use of $\Lambda (s)$ for the completed $L$-function with $\Gamma$-factors.
• $M_k(\Gamma )$, $S_k(\Gamma )$ for modular and cusp forms of weight $k$ on $\Gamma$; $T_p$ for Hecke operators.
• $T_{\ell }E$ for the $\ell$-adic Tate module; $V_\ell E := T_\ell E \otimes_{\mathbb{Z}\ell} \mathbb{Q}\ell$ for the rational version.
• ${\rho }_{f,\ell }:G_{\mathbb{Q}}\to {\mathrm{GL}}_2(\overline{{\mathbb{Q}}_{\ell }})$ for the modular Galois representation attached to a cusp eigenform $f$.

The Codex should adopt these notations verbatim (per docs/specs/UNIT_SPEC.md §11) for all 21-* units; record in a §Notation paragraph of the chapter-opening unit (21.01.01 or a chapter README).

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§5 What this plan does NOT cover

• A line-number-level inventory of every named theorem in IMNT (full P1 audit; deferred until a PDF is sourced — IMNT is 514 pp. across six chapters and three parts, and a complete inventory is a multi-week pass).
• Wiles 1995 proof of the modularity theorem at technical depth. Statement only (in 21.06.01); the full proof involves deformation theory of Galois representations, Hecke algebras, $R=\mathbb{T}$ theorems, Taylor-Wiles patching, and the numerical criterion — each of which deserves its own unit, and none of which IMNT itself develops at theorem-level proof depth. Pointer-only.
• Langlands programme at technical depth. Statement-level only (in 21.10.01); the technical content — automorphic representations of ${\mathrm{GL}}_n$, Arthur's trace formula, functoriality, the local-global Langlands correspondence — is a research-monograph subject that IMNT itself only surveys. Deferred.
• Exercise-pack production. IMNT has relatively few exercises (encyclopaedic, not textbook); exercise pack is a P3-priority-3 follow-up.
• Class field theory at proof depth. Statements only (idele class group, reciprocity); the full Tate-Artin proof via cohomology of class formations is deferred to a Neukirch-anchored unit in 21-number-theory/ not on this punch-list.
• $p$-adic Hodge theory. Fontaine's theory of $B_{\mathrm{dR}}$, $B_{\mathrm{cris}}$, $B_{\mathrm{st}}$ is touched in passing by IMNT (2nd ed.) but is a self-contained technical subject; deferred.

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§6 Acceptance criteria for FT equivalence (IMNT)

Per docs/plans/FASTTRACK_EQUIVALENCE_PLAN.md §3.4, the book is at equivalence-coverage when:

• The 21-number-theory/ chapter exists with its scaffolding (chapter README, dependency edges in docs/catalogs/DEPENDENCY_MAP.md).
• Priority-0 prerequisite units (algebraic number theory primer, local fields, étale cohomology pointer) have shipped.
• ≥95% of IMNT's surveyed theorems in Parts I + II map to Codex units (currently ~5%; after priority-1 units this rises to ~70%; after priority-1 + priority-2 to ~90%; full ≥95% requires selective priority-3).
• ≥90% of IMNT's worked computations and named conjectures have a direct unit or are referenced from a unit that covers them (Riemann hypothesis, Birch-Swinnerton-Dyer, Sato-Tate, Faltings / Mordell, modularity theorem statement, Main Conjecture statement, ABC).
• Notation decisions are recorded (see §4).
• Pass-W weaving connects the new chapter to 04-algebraic-geometry/ via the elliptic-curves unit 04.04.03, to 06-riemann-surfaces/ via the modular-group / VHS units, and (loosely) to 03-modern-geometry/ via Galois representations as principal bundles.

The 8 priority-1 units close most of the equivalence gap given the Priority-0 prereqs are in place. Priority-2 closes the Iwasawa / $p$-adic and Weil-conjectures gaps. Priority-3+4 are deepening / pointer units.

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§7 Sourcing

• Status: REDUCED. No local PDF found in the three configured paths (reference/textbooks-extra/, reference/fasttrack-texts/, reference/book-collection/free-downloads/) as of 2026-05-18. Springer link redirects to authentication; this plan was produced from canonical knowledge of IMNT's structure cross-referenced against Silverman / Diamond-Shurman / Neukirch / Bombieri-Gubler.
• Action item. Source IMNT (paid Springer or Anna's Archive) and drop into reference/textbooks-extra/ as Manin-Panchishkin-IntroductionToModernNumberTheory-2ndEd.pdf. Required before a full P1 audit can run.
• License. Springer copyright. For educational use cite as Manin, Panchishkin, Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories (Encyclopaedia of Mathematical Sciences 49, Springer-Verlag, 2nd ed. 2005).
• Local copy target path. reference/textbooks-extra/ per pattern of other paid FT texts (Hartshorne, Silverman, Neukirch).
• Companion sources already in / targeted for the reference library.
  • Silverman, The Arithmetic of Elliptic Curves — cited in 04.04.03-elliptic-curves.md; PDF status: TODO_REF.
  • Diamond-Shurman, A First Course in Modular Forms — not yet sourced; required for 21.04.* units.
  • Neukirch, Algebraic Number Theory — not yet sourced; required for Priority-0 prereq units.
  • Bombieri-Gubler, Heights in Diophantine Geometry — not yet sourced; required for 21.09.* Master-tier units.