Frobenius on the cohomology of thickenings

Author:

Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik, Anurag K. Singh, Wenliang Zhang

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Commutative Algebra (math.AC)

journal:

date:

2023-07-06 16:00:00

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.

PDF: Frobenius on the cohomology of thickenings.pdf