On the Hitchin morphism in positive characteristic

Details On the Hitchin morphism in positive characteristic On the Hitchin morphism in positive characteristic

2000-08-31

arxiv.org/abs/math/0008238v1

Mathematics

Algebraic Geometry

11 pages

Scientific paper

Let X be a smooth projective curve over a field of characteristic p>0. We show that the Hitchin morphism, which associates to a Higgs bundle its characteristic polynomial, has a non-trivial deformation over the affine line. This deformation is constructed by considering the moduli stack of t-connections on vector bundles on X and an analogue of the p-curvature, and by observing that the associated characteristic polynomial is, in a suitable sense, a p-th power.

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