Stratified bundles and Representation spaces

TL;DR

This paper constructs a special subvariety within the representation space associated with a stratified bundle on a variety, demonstrating that it contains many points coming from fundamental group representations, and provides a simplified proof of a key theorem.

Contribution

It introduces a new irreducible subvariety in the representation space linked to stratified bundles and offers a simpler proof of a significant existing theorem.

Findings

The subvariety contains a dense set of points from fundamental group representations.

The construction applies to stratified bundles over varieties.

Provides a streamlined proof of the main theorem in prior work.

Abstract

For a given stratified bundle $E$ on $X$, we construct an irreducible closed subvariety $\sN(E)_S$ of the so called representation space $R(\sO_{X_S},\xi_S,P)\to S$ such that $\sN(E)_S(\overline{\mathbb{F}}_q)$ contains a dense set of $(V,\beta)$ where $V$ is induced by a representation of $\pi_1^{{\rm \acute{e}t}}(X)$ (Theorem \ref{thm3.7}). As an application, we give a simply proof of the main theorem of \cite{EM} and its relative version (Theorem \ref{thm4.2}).