On the Hitchin morphism in positive characteristic

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 p^th-power.