On a Conjecture of Sharifi and Mazur’s Eisenstein Ideal
نویسندگان
چکیده
منابع مشابه
An Eisenstein ideal for imaginary quadratic fields and the Bloch-Kato conjecture for Hecke characters
For certain algebraic Hecke characters χ of an imaginary quadratic field F we define an Eisenstein ideal in a p-adic Hecke algebra acting on cuspidal automorphic forms of GL2/F . By finding congruences between Eisenstein cohomology classes (in the sense of G. Harder) and cuspidal classes we prove a lower bound for the index of the Eisenstein ideal in the Hecke algebra in terms of the special L-...
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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,...
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We use pseudodeformation theory to study Mazur’s Eisenstein ideal. Given prime numbers N and p > 3, we study the Eisenstein part of the p-adic Hecke algebra for Γ0(N). We compute the rank of this Hecke algebra in terms of Massey products in Galois cohomology, answering a question of Mazur and generalizing a result of Calegari-Emerton. We also also give new proofs of Merel’s result on this rank ...
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Let E(p) denote the Eisenstein ideal in the Hecke algebra T(p) of the Drinfeld modular curve X0(p) parameterizing Drinfeld modules of rank two over Fq[T ] of general characteristic with Hecke level p-structure, where p⊳ Fq[T ] is a nonzero prime ideal. We prove that the characteristic p of the field Fq does not divide the order of the quotient T(p)/E(p) and the Eisenstein ideal E(p) is locally ...
متن کاملOn the Eisenstein ideal for imaginary quadratic fields
For certain algebraic Hecke characters χ of an imaginary quadratic field F we define an Eisenstein ideal in a p-adic Hecke algebra acting on cuspidal automorphic forms of GL2/F . By finding congruences between Eisenstein cohomology classes (in the sense of G. Harder) and cuspidal classes we prove a lower bound for the index of the Eisenstein ideal in the Hecke algebra in terms of the special L-...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2020
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnaa115