Modular Forms, Hecke Operators, and Modular Abelian Varieties
by Kenneth A. Ribet, William A. Stein
Publisher: University of Washington 2003
Number of pages: 154
Contents: The Main objects; Modular representations and algebraic curves; Modular Forms of Level 1; Analytic theory of modular curves; Modular Symbols; Modular Forms of Higher Level; Newforms and Euler Products; Hecke operators as correspondences; Abelian Varieties; Abelian Varieties Attached to Modular Forms; L-functions; The Birch and Swinnerton-Dyer Conjecture.
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This book provides a review of an important aspect of the geometric Langlands program - the role of representation theory of affine Kac-Moody algebras. It provides introductions to such notions as vertex algebras, the Langlands dual group, etc.
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