An explicit example of Frobenius periodicity
Holger Brenner, Almar Kaid

TL;DR
This paper demonstrates a specific Frobenius periodicity for the restriction of the cotangent bundle on Fermat curves in certain characteristics, revealing explicit examples of Frobenius periodicity in algebraic geometry.
Contribution
It provides an explicit example of Frobenius periodicity for vector bundles on Fermat curves in characteristic p, expanding understanding of Frobenius behavior in algebraic geometry.
Findings
Frobenius pull-back of the bundle is isomorphic to the bundle itself up to tensoring.
The result applies to Fermat curves of degree 2d in characteristic p ≡ -1 mod 2d.
Establishes a concrete example of Frobenius periodicity for a class of vector bundles.
Abstract
In this note we show that the restriction of the cotangent bundle of the projective plane to a Fermat curve of degree in characteristic is, up to tensoration with a certain line bundle, isomorphic to its Frobenius pull-back. This leads to a Frobenius periodicity on the Fermat curve of degree 2d, where .
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology
