Galois representations
Galois representations, embedding problems and modular forms.
To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations...
Galois representations, Hecke operators, and the cohomology of with twisted coefficients.
Galois representations into GL2(Zp[[X]]) attached to ordinary cusp forms.
Galois representations modulo p and cohomology of Hilbert modular varieties
Galois representations of dihedral type over ℚₚ
Global quadratic units and Hecke algebras.
Growth of Selmer groups of Hilbert modular forms over ring class fields
We prove non-trivial lower bounds for the growth of ranks of Selmer groups of Hilbert modular forms over ring class fields and over certain Kummer extensions, by establishing first a suitable parity result.