Frobenius on the Cohomology of Thickenings-Reference-Cited by-同舟云学术

Frobenius on the Cohomology of Thickenings

Published:2023-12-28 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Bhatt Bhargav¹,Blickle Manuel²,Lyubeznik Gennady³,Singh Anurag K⁴,Zhang Wenliang⁵

Affiliation:

1. Mathematics IAS/Princeton University , Princeton, USA and Department of Mathematics, University of Michigan, Ann Arbor, USA

2. Institut für Mathematik , Johannes Gutenberg-Universität Mainz, Mainz, Germany

3. School of Mathematics, University of Minnesota , Minneapolis, USA

4. Department of Mathematics,University of Utah , Salt Lake City, USA

5. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago , Chicago, USA

Abstract

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.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnad291/54915710/rnad291.pdf

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