Initial Zotero textbook checklist shortlist preserved verbatim

Yes. The live Zotero library contains several strong checklist sources. All items below have PDFs and Markdown extractions.

Best next checklists

  1. Modules and rings
    • Zotero LGNAU2R4
    • Citekey Lam99
    • T. Y. Lam, Lectures on Modules and Rings
    • Covers projective, injective, free, flat, semisimple, Noetherian, Artinian, and finite-length modules.
    • This is the best source for the current module-category residue.
  2. Commutative algebra beyond Atiyah-Macdonald
    • Zotero 72SP2PMS
    • Citekey MR92
    • Hideyuki Matsumura and Miles Reid, Commutative Ring Theory
    • Covers dimension, regular sequences, depth, Cohen-Macaulay rings, completions, and local algebra.
  3. Commutative algebra for algebraic geometry
    • Zotero XM34VXLW
    • Citekey Eis95
    • David Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry
    • Adds resolutions, syzygies, graded rings, Hilbert functions, depth, and multiplicity.
  4. Ordinary category theory
    • Zotero SK2Y8WNL
    • Citekey Mac98
    • Saunders Mac Lane, Categories for the Working Mathematician
    • Gives a canonical checklist for categories, functors, natural transformations, adjunctions, Kan extensions, limits, monads, and monoidal categories.
  5. Modern ordinary category theory
    • Zotero TIDLVIT4
    • Citekey Rie16
    • Emily Riehl, Category Theory in Context
    • This is probably the clearest primary checklist for the project’s standard categorical vocabulary.
  6. Higher-category foundations
    • Zotero TS95LIXR
    • Citekey RV22
    • Emily Riehl and Dominic Verity, Elements of ∞-Category Theory
    • Relevant to homotopy pullbacks, higher cells, equivalences, adjunctions, and limits of higher categories.
  7. Homological algebra
    • Zotero 8XN9IJSP
    • Citekey Wei94
    • Charles Weibel, An Introduction to Homological Algebra
    • Covers complexes, homotopy, homology, derived functors, Ext, Tor, resolutions, spectral sequences, and derived categories.
  8. Schemes and local algebra
    • Zotero ESZQ6XYL
    • Citekey Vak25
    • Ravi Vakil, The Rising Sea: Foundations of Algebraic Geometry
    • The best large checklist for spectra, sheaves, schemes, stalks, fiber products, morphism properties, divisors, and cohomology.
  9. Algebraic number theory
    • Zotero 8698XMKC
    • Citekey Neu99
    • Jürgen Neukirch and Norbert Schappacher, Algebraic Number Theory
    • Covers number rings, fractional ideals, valuations, completions, local fields, adeles, ideles, and class groups.
  10. Local fields
    • Zotero 2K45J388
    • Citekey Ser79
    • Jean-Pierre Serre, Local Fields
    • Gives a compact checklist for discrete valuations, ramification, completions, unit filtrations, local extensions, and local class field theory.
  11. Bilinear forms over rings
    • Zotero 3M28YXGC
    • Citekey MH73
    • John Milnor and Dale Husemöller, Symmetric Bilinear Forms
    • Highly relevant to formed modules, radicals, duals, unimodularity, localization, Witt groups, and integral forms.
  12. Quadratic forms
    • Zotero 58GTJTDZ
    • Citekey OM00
    • O. Timothy O’Meara, Introduction to Quadratic Forms
    • Strong source for lattices, modularity, local theory, Jordan decompositions, genus, and equivalence.

Useful secondary checklists

  • Zotero HMSEFIXJ, citekey Ger08: Larry Gerstein, Basic Quadratic Forms. A smaller first checklist than O’Meara.
  • Zotero BA56XQA6, citekey Cas08a: J. W. S. Cassels, Rational Quadratic Forms. Best for field-valued quadratic forms and local-global theory.
  • Zotero T2WVLTDB, citekey CS10: Conway and Sloane, Sphere Packings, Lattices and Groups. Useful for lattice terminology and examples, but not foundational algebra.
  • Zotero D6XUJE8G, citekey Wei82: André Weil, Adeles and Algebraic Groups. Useful for the adelic checklist, but not a basic first source.
  • Zotero 4M9EBKXL, citekey Liu10: Qing Liu, Algebraic Geometry and Arithmetic Curves. Best after the basic scheme vocabulary exists.
  • Zotero EHRS7CWC, citekey Bou83: Bourbaki, Algèbre Commutative. Encyclopedic reference, but less convenient as the first checklist.
  • Zotero WSSX45DL, citekey Lan05: Serge Lang, Algebra. Useful for a broad algebra catalogue, but much wider than the current residue.

The highest-value sequence is: Lam99, MR92, Rie16, Wei94, Vak25, Neu99, Ser79, MH73, then OM00.