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- Title
Frobenius on the Cohomology of Thickenings.
- Authors
Bhatt, Bhargav; Blickle, Manuel; Lyubeznik, Gennady; Singh, Anurag K; Zhang, Wenliang
- 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—that is, 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.
- Subjects
ELLIPTIC curves; PROJECTIVE spaces; HYPERSURFACES; INJECTIVE functions
- Publication
IMRN: International Mathematics Research Notices, 2024, Vol 2024, Issue 10, p8557
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnad291