I think the articles and books below are the most important references for
learning about modular abelian varieties. Click on the link for more information
about each book.
Modular Curves and Modular Forms
- Ribet-Stein, Lectures on Serre's Conjectures
- Diamond and Im, Modular forms and modular curves
(in particular, Part I, Part II Sections 7, 9.1, 9.2, 10.1)
- Darmon, Diamond, Taylor, Fermat's Last Theorem
- Knapp, Elliptic curves
- Lang, Introduction to Modular Forms
- Manin, Parabolic points and zeta functions
of modular curves
- Miyake, Modular forms
- Ribet, Galois Representations and Modular Forms
- Serre, A course in arithmetic (chapter 7)
- Shimura, Introduction to the Arithmetic
Theory of Automorphic Functions
Abelian Varieties and Jacobians
- Lang, Introduction to Algebraic and Abelian Functions
- Lang, Abelian Varieties (second edition)
- Milne, Abelian Varieties (mainly Sections 1, 2,
7, 8, 9, 10, 11, 12, 16, 19)
- Milne, Jacobian Varieties (Sections 1-6 and
10)
- Mumford. Abelian Varieties
- Mumford, Curves and their Jacobians
- Rosen, Abelian Varieties over C
- Swinnerton-Dyer, Analytic theory of abelian
varieties
Modular Abelian Varieties
The Birch and Swinnerton-Dyer Conjecture
- Artin, Neron Models (Sections 1 and 2), in Cornell-Silverman
- Birch, Conjectures Concerning Elliptic Curves
- Birch, Elliptic curves over Q,
A Progress Report
- Kolyvagin, Bounding Selmer Groups via the Theory of Euler Systems (Section
0 only)
- Lang, Number Theory III
- Rubin, The work of Kolyvagin on the arithmetic
of elliptic curves
- Tate, The Birch and Swinnerton-Dyer Conjecture and a
Geometric Analogue
- Swinnerton-Dyer, The Conjectures of Birch
and Swinnerton-Dyer, and of Tate
- Silverman,The Theory of Height Functions (Sections 1-5), in Cornell-Silverman
- Wiles, The Birch and Swinnerton-Dyer Conjecture
(for Clay Math Institute)
Computation
- Cremona, Algorithms for Modular Elliptic Curves,
2nd edition
- Flynn, Leprevost, Schaefer, Stein, Stoll and Wetherell, Empirical
evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians
of genus 2 curves
- Merel, Universal Fourier Expansions of Modular
Forms
- Stein, An introduction to computing modular
forms using modular symbols
- Stein, Studying the Birch and Swinnerton-Dyer
Conjecture for Modular Abelian Varieties Using MAGMA
- Stein, MAGMA documentation for modular forms and modular
symbols
Other Related References
