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MODULARITY OF CERTAIN POTENTIALLY BARSOTTI-TATE GALOIS REPRESENTATIONS
CERTAIN POTENTIALLY REPRESENTATIONS
2015/7/6
where is the reduction of . These results were subject to hypotheses on the local
behavior of at `, i.e., the restriction of to a decomposition group at `, and to
irreducibility hypotheses on...
On the Surjectivity of Galois Representations Associated to Elliptic Curves over Number Fields
Surjectivity Galois Representations Elliptic Curves over Number Fields Number Theory
2012/4/17
Given an elliptic curve $E$ over a number field $K$, the $\ell$-torsion points $E[\ell]$ of $E$ define a Galois representation $\gal(\bar{K}/K) \to \gl_2(\ff_\ell)$. A famous theorem of Serre states t...
On the automorphy of $l$-adic Galois representations with small residual image
small residual image Galois representations Number Theory
2011/9/23
Abstract: We prove new automorphy lifting theorems for essentially conjugate self-dual Galois representations into $GL_n$. Existing theorems require that the residual representation have 'big' image, ...
Even Galois Representations and the Fontaine--Mazur conjecture II
Even Galois Representations Fontaine--Mazur conjecture II
2011/2/24
We prove, under mild hypotheses, that there are no irreducible two-dimensional po-tentially semi-stable even p-adic Galois representations of Gal(Q/Q) with distinct Hodge–Tate weights.
The Galois representation associated to a p-divisible group over a noetherian complete local domain with perfect residue field is described in terms of its Dieudonn´e display.
An effective isomorphy criterion for mod $\ell$ Galois representations
effective isomorphy criterion mod $\ell$ Galois representations
2010/12/15
In this paper, we consider mod ℓ Galois representations of Q. In particular, we obtain an effective criterion to distinguish two semisimple 2-dimensional, odd mod ℓ Galois representations ...
The conjectural connections between automorphic representations and Galois representations
conjectural connections between automorphic representations Galois representations
2010/11/30
We state conjectures on the relationships between automorphic representations and Galois representations, and give evidence for them.