Krzysztof Klosin

A deformation problem for Galois representations over imaginary quadratic fields

We prove the modularity of minimally ramified ordinary residually reducible p-adic Galois representations of an imaginary quadratic field F under certain assumptions. We first exhibit conditions under which the residual representation is unique up to isomorphism. Then we prove the existence of deformations arising from cuspforms on GL2(AF ) via the Galois representations constructed by Taylor et al. We establish a sufficient condition (in terms of the non-existence of certain field extensions which in many cases can be reduced to a condition on an L-value) for the universal deformation ring to be a discrete valuation ring and in that case we prove an R = T theorem. We also study reducible deformations and show that no minimal characteristic 0 reducible deformation exists.

On Lifting and Modularity of Reducible Residual Galois Representations Over Imaginary Quadratic Fields

In this paper we study deformations of mod

The Maass space for U (2,2) and the Bloch–Kato conjecture for the symmetric square motive of a modular form

p

On higher congruences between automorphic forms

Galois representations

On deformation rings of residually reducible Galois representations and R = T theorems

\tau

An R= T theorem for imaginary quadratic fields

(over an imaginary quadratic field

Adelic Maass spaces on U(2,2)

F

Deformations of Saito-Kurokawa type and the Paramodular Conjecture (with an appendix by Cris Poor, Jerry Shurman, and David S. Yuen)

) of dimension

Modularity of residual Galois extensions and the Eisenstein ideal.

2

A p-adic Hermitian Maass lift

whose semi-simplification is the direct sum of two characters