Hitchin pairs on an integral curve

Abstract

Let Y be an integral projective scheme of dimension 1 over a field k (of arbitrary characteristic). We construct the moduli spaces of Hitchin pairs on Y. We define a notion of strong semistability for Hitchin pairs on Y. Assume that the base field is infinite and the normalization of Y is smooth. Then we show that finite direct sums of strongly semistable Hitchin pairs on Y form a neutral Tannakian category. We define the holonomy group scheme G^H_Y of Y to be the Tannakian group scheme for this category. For a strongly semistable G-Hitchin pair, we construct a monodromy group scheme. We study the relation between Higgs bundles on Y and the representations of the (topological) fundamental group of Y in the complex general linear group.