The de Rham cohomology of p-group covers
24 months
Institute of Mathematics of Polish Academy of Sciences
in the project I will study algebraic curves, their symmetries and invariants (cohomologies).
p-group Galois covers of curves in characteristic p II - in this article we give a connection between the equivariant structure of cohomologies of a G-cover and HKG-covers. As an application, we compute the de Rham cohomology of a Klein cover.
The “exponential” torsion of superelliptic Jacobians - in this article we study the l-power torsion of the Jacobian of the curve y^l = f(x). As an application we prove the Hodge, Tate and Mumford-Tate conjectures for the considered Jacobians.
Indecomposable direct summands of cohomologies of curves - In this article we explore the possible “building blocks” (the indecomposable direct summands) of cohomologies of smooth projective curves with a group action. We show that usually there are infinitely many such possible summands.