Stable bundles as Frobenius morphism direct image

Abstract

Let X be a smooth projective curve of genus $g\ge 2$ defined over an algebraically closed field k of characteristic $p>0$ and let $F:X\to X_1$ be the relative k-linear Frobenius map. We prove (Theorem 1.1) E is a stable bundle on $X_1$ with $I(E)=(p-1)(2g-2)$ if and only if E is the direct image of some stable bundle W on $X$.

4 pages