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International Mathematics Research Notices (2001) 2001:129-143, doi:10.1155/S1073792801000071
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Copyright © 2001 Hindawi Publishing Corporation. All rights reserved.

On the Hitchin morphism in positive characteristic

Yves Laszlo and Christian Pauly

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 nontrivial 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 pth-power.


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