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...

Let V be a de-Rham representation of the Galois group of a local field of mixed characteristic (0, p). We relate the Swan conductor of the associated Weil-Deligne representation to the irregularity of the corresponding p-adic differential equation. 2000 Mathematics Subject Classification: 11F80,11F85,11S15,12H25

We generalize the result of [11] on incompressibility of Galois Weil transfer of generalized Severi-Brauer varieties, to direct products of varieties of such type; as shown in [11], this is needed to compute essential dimension of representations of finite groups. We also provide a generalization to non-Galois (separable) Weil transfer.

We classify representations of a class Deligne-Mostow lattices into PGL(3,C). In particular, we show local rigidity for the (of with three-fold symmetry and type one) where generators chose are same as lattices. also without constraints on six them existence deformations number in three them. use formal computations SAGE Maple to obtain results. The code files available GitHub ([7]).

In [12] and [13], Silverman discusses the problem of bounding the Mordell-Weil ranks of elliptic curves over towers of function fields. We first prove generalizations of the theorems of those two papers by a different method, allowing non-abelian Galois groups and removing the dependence on Tate’s conjectures. We then prove some theorems about the growth of Mordell-Weil ranks in towers of funct...

We combine the geometric realization of principal series representations of [28] with the Bott–Borel–Weil Theorem for direct limits of compact groups found in [22], obtaining limits of principal series representations for direct limits of real reductive Lie groups. We introduce the notion of weakly parabolic direct limits and relate it to the conditions that the limit representations are norm–p...

The braid group of n-strings is the group of homotopy types of movements of n distinct points in the 2-plane R. It was introduced by E. Artin [1] in 1926 in order to study knots in R. He gave a presentation of the braid group by generators and relations, which are, nowadays, called the Artin braid relations. Since then, not only in the study of knots, the braid groups appear in several contexts...

Let G be a reductive group over a finite field Fq and let G(Fq) be its group of Fq-rational points. In 1976 P. Deligne and G. Lusztig (following a suggestion of V. Drinfeld for G = SL(2)) associated to any maximal torus T in G defined over Fq certain remarkable series (virtual) representations of the group G(Fq). These representations were realized in é tale l-adic cohomology of certain algebra...