Wojciech J. Gajda

Abstract:

The de Rham cohomology of any smooth complex projective variety decomposes as a direct sum of pieces coming from the Hodge cohomology. For algebraic varieties over general fields this decomposition may be replaced by a spectral sequence. In many cases this spectral sequence degenerates on the first page providing us the Hodge-de Rham exact sequence. During the talk we will consider this exact sequence for an algebraic variety with a group action. We will investigate when does this sequence split equivariantly, using the group cohomology of sheaves. Also, we will tie this problem to lifting coverings of curves to the ring of Witt vectors of length 2.