Abstract

Consider a smooth projective curve over a field of positive characteristic. Attached to every rank-r vector bundle of degree 0 on this curve is a twisted endomorphism called the Higgs field. The Hitchin morphism associates to each Higgs field its characteristic polynomial. In this talk, we will consider generalizations of Higgs fields, called t-connections. Using nice functorial properties of the sheaf of principal parts and the relative Frobenius, we will discuss some geometric properties of the moduli stack of t-connections on vector bundles on our curve. Then, we will construct a suitable analogue of the p-curvature and observe that its characteristic polynomial is in some sense a pth-power, and that its restriction to a fiber coincides with the Hitchin morphism.