Frobenius on the cohomology of thickenings
Algebraic Geometry
2023-07-10 v1 Commutative Algebra
Abstract
We investigate the injectivity of the Frobenius map on thickenings of smooth varieties in projective space over a field of positive characteristic. We obtain uniform bounds -- i.e., independent of the characteristic -- on the thickening that ensures an injective Frobenius map when the projective variety is a smooth complete intersection or an arbitrary projective embedding of an elliptic curve. Our bounds are sharp in the case of hypersurfaces, and in the case of elliptic curves.
Keywords
Cite
@article{arxiv.2307.03745,
title = {Frobenius on the cohomology of thickenings},
author = {Bhargav Bhatt and Manuel Blickle and Gennady Lyubeznik and Anurag K. Singh and Wenliang Zhang},
journal= {arXiv preprint arXiv:2307.03745},
year = {2023}
}
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