An explicit example of Frobenius periodicity

Details An explicit example of Frobenius periodicity An explicit example of Frobenius periodicity

2010-11-18

arxiv.org/abs/1011.4186v1

Mathematics

Algebraic Geometry

Scientific paper

In this note we show that the restriction of the cotangent bundle $\Omega_{\mathbb P}^2$ of the projective plane to a Fermat curve $C$ of degree $d$ in characteristic $p \equiv -1 \mod 2d$ is, up to tensoration with a certain line bundle, isomorphic to its Frobenius pull-back. This leads to a Frobenius periodicity $F^*({\mathcal E}) \cong {\mathcal E} $ on the Fermat curve of degree $2d$, where ${\mathcal E}= {\rm Syz}(U^2,V^2,W^2)(3)$.

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