Exponential sums and rigid cohomology

TL;DR

This paper establishes a comparison between Dwork cohomology and rigid cohomology, enabling explicit calculation of the latter for Dwork isocrystals on tori, thus advancing understanding in p-adic cohomological theories.

Contribution

It proves a comparison theorem linking Dwork and rigid cohomology, facilitating computations of rigid cohomology for Dwork isocrystals on tori.

Findings

Established a comparison theorem between Dwork and rigid cohomology.

Enabled explicit calculation of rigid cohomology for Dwork isocrystals.

Provided new tools for p-adic cohomological analysis.

Abstract

In this article, we prove a comparison theorem between the Dwork cohomology introduced by Adolphson and Sperber and the rigid cohomology. As a corollary, we can calculate the rigid cohomology of Dwork isocrystal on torus.