Galois representations of dihedral type over Qp
نویسندگان
چکیده
منابع مشابه
Dihedral Galois Representations and Katz Modular Forms
We show that any two-dimensional odd dihedral representation ρ over a finite field of characteristic p > 0 of the absolute Galois group of the rational numbers can be obtained from a Katz modular form of level N , character 2 and weight k, where N is the conductor, 2 is the prime-to-p part of the determinant and k is the so-called minimal weight of ρ. In particular, k = 1 if and only if ρ is un...
متن کاملA CLASS OF p-ADIC GALOIS REPRESENTATIONS ARISING FROM ABELIAN VARIETIES OVER Qp
Let V be a p-adic representation of the absolute Galois group G of Qp that becomes crystalline over a finite tame extension, and assume p 6= 2. We provide necessary and sufficient conditions for V to be isomorphic to the p-adic Tate module Vp(A) of an abelian variety A defined over Qp. These conditions are stated on the filtered (φ,G)module attached to V . 2000 Mathematics Subject Classificatio...
متن کاملModularity of Nearly Ordinary 2-adic Residually Dihedral Galois Representations
We prove modularity of some two dimensional, 2-adic Galois representations over a totally real field that are nearly ordinary at all places above 2 and that are residually dihedral. We do this by employing the strategy of Skinner and Wiles, using Hida families, together with the 2-adic patching method of Khare and Wintenberger. As an application we deduce modularity of some elliptic curves over...
متن کاملDeformation of Outer Representations of Galois Group
To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than t...
متن کاملDeformation of Outer Representations of Galois Group II
This paper is devoted to deformation theory of "anabelian" representations of the absolute Galois group landing in outer automorphism group of the algebraic fundamental group of a hyperbolic smooth curve defined over a number-field. In the first part of this paper, we obtained several universal deformations for Lie-algebra versions of the above representation using the Schlessinger criteria for...
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: Acta Arithmetica
سال: 2004
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa111-1-4