Author | Hida, Haruzo. author |
---|---|
Title | p-Adic Automorphic Forms on Shimura Varieties [electronic resource] / by Haruzo Hida |
Imprint | New York, NY : Springer New York, 2004 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-9390-0 |
Descript | XI, 390 p. online resource |
1 Introduction -- 1.1 Automorphic Forms on Classical Groups -- 1.2 p-Adic Interpolation of Automorphic Forms -- 1.3 p-Adic Automorphic L-functions -- 1.4 Galois Representations -- 1.5 Plan of the Book -- 1.6 Notation -- 2 Geometric Reciprocity Laws -- 2.1 Sketch of Classical Reciprocity Laws -- 2.2 Cyclotomic Reciprocity Laws and Adeles -- 2.3 A Generalization of Galois Theory -- 2.4 Algebraic Curves over a Field -- 2.5 Elliptic Curves over a Field -- 2.6 Elliptic Modular Function Field -- 3 Modular Curves -- 3.1 Basics of Elliptic Curves over a Scheme -- 3.2 Moduli of Elliptic Curves and the Igusa Tower -- 3.3 p-Ordinary Elliptic Modular Forms -- 3.4 Elliptic ?-Adic Forms and p-Adic L-functions -- 4 Hilbert Modular Varieties -- 4.1 HilbertโBlumenthal Moduli -- 4.2 Hilbert Modular Shimura Varieties -- 4.3 Rank of p-Ordinary Cohomology Groups -- 4.4 Appendix: Fundamental Groups -- 5 Generalized EichlerโShimura Map -- 5.1 Semi-Simplicity of Hecke Algebras -- 5.2 Explicit Symmetric Domains -- 5.3 The EichlerโShimura Map -- 6 Moduli Schemes -- 6.1 Hilbert Schemes -- 6.2 Quotients by PGL(n) -- 6.3 Mumford Moduli -- 6.4 Siegel Modular Variety -- 7 Shimura Varieties -- 7.1 PEL Moduli Varieties -- 7.2 General Shimura Varieties -- 8 Ordinary p-Adic Automorphic Forms -- 8.1 True and False Automorphic Forms -- 8.2 Deformation Theory of Serre and Tate -- 8.3 Vertical Control Theorem -- 8.4 Irreducibility of Igusa Towers -- References -- Symbol Index -- Statement Index