## Speaker:

Daxin Xu

## Speaker Link:

## Institution:

Caltech

## Time:

Thursday, November 15, 2018 - 3:00pm

Let k be a perfect field of characteristic p > 0 and W the ring of Witt vectors of k. In this talk, we give a new proof of the Frobenius descent for convergent isocrystals on a variety over k relative to W. This proof allows us to deduce an analogue of the de Rham complexes comparison theorem of Berthelot without assuming a lifting of the Frobenius morphism. As an application, we prove a version of Berthelot's conjecture on the preservation of convergent isocrystals under the higher direct image by a smooth proper morphism of k-varieties in the context of Ogus' convergent topos.