An explicit example of Frobenius periodicity

In this paper we show that the restriction of the cotangent bundle ΩP2 of the projective plane to a Fermat curve C of degree d in characteristic p≡−1mod2d is, up to tensoration with a certain line bundle, isomorphic to its Frobenius pull-back. This leads to a Frobenius periodicity F∗(E)≅E on the Fermat curve of degree 2d, where .