Eisenstein Hecke Algebras and Conjectures in Iwasawa Theory
نویسنده
چکیده
We formulate a weak Gorenstein property for the Eisenstein component of the p-adic Hecke algebra associated to modular forms. We show that this weak Gorenstein property holds if and only if a weak form of Sharifi’s conjecture and a weak form of Greenberg’s conjecture hold.
منابع مشابه
Selmer Groups and the Eisenstein-klingen Ideal
0 Introduction The central point in the Bloch-Kato conjectures is to establish formulas for the order of the Selmer groups attached to Galois representations in terms of the special values of their L-functions. In order to give upper bound, the main way is to construct Euler systems following Kolyvagin. Besides, lower bounds have been obtained by using congruences between automorphic forms. So,...
متن کاملEisenstein Congruence on Unitary Groups and Iwasawa Main Conjectures for Cm Fields
Introduction 1 1. Notation and conventions 8 2. Shimura varieties for unitary groups 13 3. Modular forms on unitary groups 23 4. Hida theory for unitary groups 36 5. Ordinary p-adic Eisenstein series on U(2, 1) 52 6. Constant terms of the p-adic Eisenstein series 68 7. Eisenstein ideal and p-adic L-functions 76 8. Application to the main conjecture for CM fields 93 Acknowledgments 107 Reference...
متن کاملArithmetic Teichmuller Theory
By Grothedieck's Anabelian conjectures, Galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth curves defined over number fields encode all arithmetic information of these curves. The goal of this paper is to develope and arithmetic teichmuller theory, by which we mean, introducing arithmetic objects summarizing th...
متن کاملCrystals and Affine Hecke Algebras of Type D
The Lascoux-Leclerc-Thibon-Ariki theory asserts that the K-group of the representations of the affine Hecke algebras of type A is isomorphic to the algebra of functions on the maximal unipotent subgroup of the group associated with a Lie algebra g where g is gl ∞ or the affine Lie algebra A (1) l , and the irreducible representations correspond to the upper global bases. Recently, N. Enomoto an...
متن کامل2 Hecke Algebras with Unequal Parameters
These notes are an expanded version of the Aisenstadt lectures given at the CRM, Université de Montréal, in May/June 2002; they also include material from lectures given at MIT during the Fall of 1999 [L12]. I wish to thank Jacques Hurtubise for inviting me to give the Aisenstadt lectures. Hecke algebras arise as endomorphism algebras of representations of groups induced by representations of s...
متن کامل