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The Frobenius action on rank $2$ vector bundles over curves in small genus and small characteristic

Laurent Ducrohet — 2009

Annales de l’institut Fourier

Let $X$ be a general proper and smooth curve of genus $2$ (resp. of genus $3$ ) defined over an algebraically closed field of characteristic $p$ . When $3 \leq p \leq 7$ , the action of Frobenius on rank $2$ semi-stable vector bundles with trivial determinant is completely determined by its restrictions to the 30 lines (resp. the 126 Kummer surfaces) that are invariant under the action of some order $2$ line bundle over $X$ . Those lines (resp. those Kummer surfaces) are closely related to the elliptic curves (resp. the abelian...

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The Frobenius action on rank 2 vector bundles over curves in small genus and small characteristic

The Frobenius action on rank $2$ vector bundles over curves in small genus and small characteristic