The generalized Verschiebung map for curves of genus 2
Abstract
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.
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