Tensor product theorem for Hitchin pairs -An algebraic approach

TL;DR

This paper presents an algebraic method to prove the tensor product theorem for Hitchin pairs, establishing stability properties over smooth projective curves in various characteristics.

Contribution

It introduces an algebraic approach to the tensor product theorem for Hitchin pairs, extending results to both semistable and polystable cases in different characteristics.

Findings

Proves tensor product theorem for Hitchin pairs in characteristic 0 and p.

Establishes stability properties for Higgs semistable Hitchin pairs.

Extends results to polystable bundles.

Abstract

We give an algebraic approach to the study of Hitchin pairs and prove the tensor product theorem for Higgs semistable Hitchin pairs over smooth projective curves defined over algebraically closed fields $k$ of characteristic $0$ and characteristic $p$, with $p$ satisfying some natural bounds. We also prove the corresponding theorem for polystable bundles.