Adjoint modular Galois representations and their Selmer groups
نویسندگان
چکیده
منابع مشابه
Deformations of Hilbert Modular Galois Representations and Adjoint Selmer Groups
We prove the vanishing of the geometric Bloch–Kato Selmer group for the adjoint representation of a Galois representation associated to a Hilbert modular form under mild assumptions on the residual image. In particular, we do not assume the residual image satisfies the Taylor–Wiles hypothesis. Using this, we deduce that the localization and completion of the universal deformation ring for the r...
متن کاملDeformations of Polarized Automorphic Galois Representations and Adjoint Selmer Groups
We prove the vanishing of the geometric Bloch–Kato Selmer group for the adjoint representation of a Galois representation associated to regular algebraic polarized cuspidal automorphic representations under an assumption on the residual image. Using this, we deduce that the localization and completion of a certain universal deformation ring for the residual representation at the characteristic ...
متن کاملOn the Galois Structure of Selmer Groups
Let A be an abelian variety defined over a number field k and F a finite Galois extension of k. Let p be a prime number. Then under certain not-too-stringent conditions on A and F we investigate the explicit Galois structure of the p-primary Selmer group of A over F . We also use the results so obtained to derive new bounds on the growth of the Selmer rank of A over extensions of k.
متن کاملGalois representations and modular forms
This note is based on a series of lectures given at the summer school held on July 17-29, 2006 at IHES. The purpose of the lectures is to explain the basic ideas in the geometric construction of the Galois representations associated to elliptic modular forms of weight at least 2.
متن کاملGalois Representations and Modular Forms
In this article, I discuss material which is related to the recent proof of Fermat's Last Theorem: elliptic curves, modular forms, Galois representations and their deformations, Frey's construction, and the conjectures of Serre and of Taniyama-Shimura.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1997
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.94.21.11121