The generalized Verschiebung map for curves of genus 2

الأصل · EN

Let C be a smooth curve, and Mᵣ(C) the coarse moduli space of vector bundles of rank r and trivial determinant on C. We examine the generalized Verschiebung map Vᵣ: Mᵣ(C(p)) --> Mᵣ(C) induced by pulling back under Frobenius. Our main result is a computation of the degree of V₂ for a general C of genus 2, in characteristic p>2. We also give several general background results on the Verschiebung in an appendix.