The generalized Verschiebung map for curves of genus 2

@article{Osserman2004TheGV,
  title={The generalized Verschiebung map for curves of genus 2},
  author={Brian Osserman},
  journal={Mathematische Annalen},
  year={2004},
  volume={336},
  pages={963-986}
}
AbstractLet 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 $$V_{r}: M_{r}(C^{(p)}) \dashrightarrow M_{r}(C)$$ 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.