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 <= p <= 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 surfaces) that appear as the Prym varieties associated to double etale coverings of X. We are therefore able to compute the explicit, equations defining Frobenius action in these cases. We perform some of these computations and draw some geometric consequences.
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