  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.
