Twisted Higgs bundles and coendoscopy

TL;DR

This paper investigates twisted G-Higgs bundles influenced by central gerbes, demonstrating their stability in point-counts and cohomology, and extends Ngô's product formula to twisted Hitchin fibres.

Contribution

It introduces the concept of G-Higgs bundles twisted by a central gerbe and proves their invariance in key invariants, extending Ngô's product formula to this new setting.

Findings

Stabilized point-counts are unaffected by the central twist.

Cohomology remains insensitive to the twisting by a central gerbe.

An analogue of Ngô's product formula is established for twisted Hitchin fibres.

Abstract

This short note is devoted to the study of $G$-Higgs bundles twisted by a central gerbe. These objects arise naturally in the decomposition of the inertia stacks of $G$-Higgs bundles in terms of coendoscopic data. We establish that stabilised point-counts and cohomology are insensitive to the central twist. Along the way we show an analogue of Ng\^o's product formula for twisted Hitchin fibres.