Sonatina

Title of the project:

The de Rham cohomology of p-group covers

Duration:

24 months

Hosting Institution:

Institute of Mathematics of Polish Academy of Sciences

Short description:

in the project I will study algebraic curves, their symmetries and invariants (cohomologies).

• Description for the general public
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Results of the project:

• 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.