The action of the Frobenius map on rank 2 vector bundles over a supersingular genus 2 curve in characteristic 2

Abstract

We compute the equations of the Frobenius action on semi-stable rank 2 vector bundles with trivial determinant over a supersingular, proper and smooth, curve of genus 2, defined over an algebraically closed field of characteristic 2 and draw some geometric consequences. The computation strategy is to deform the situation to an ordinary curve where we can use the results of Y. Laszlo and C. Pauly.