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The generalized Verschiebung map for curves of genus 2

Brian Osserman
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Abstract

Let C be a smooth curve, and M_r(C) the coarse moduli space of vector bundles of rank r and trivial determinant on C. We examine the generalized Verschiebung map V_r: M_r(C^(p)) --> M_r(C) induced by pulling back under Frobenius. Our main result is a computation of the degree of V_2 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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Brian Osserman. 2004-10-29. The generalized Verschiebung map for curves of genus 2. https://arxiv.org/abs/math/0410613

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