Hodge cohomology of \'etale Nori finite vector bundles

TL;DR

This paper investigates the Hodge cohomology of étale Nori finite vector bundles, showing that their cohomology dimensions remain invariant under certain field automorphisms, thus generalizing previous results to higher ranks.

Contribution

It extends Pink-Roessler's result to higher rank vector bundles, demonstrating invariance of Hodge cohomology dimensions under field automorphisms for a broad class of bundles.

Findings

Hodge cohomology dimensions are invariant under automorphisms of the ground field.

The invariance result applies to many cases of étale Nori finite vector bundles.

Generalization of Pink-Roessler's result to higher rank bundles.

Abstract

\'Etale Nori finite vector bundles are those bundles defined by representations of a finite \'etale group scheme in the usual way. In this note we show that in many cases the dimensions of the Hodge cohomology groups of such a vector bundle and of a twist of it by an automorphism of the ground field are the same. This generalizes to the higher rank case a result of Pink-Roessler.