Global Frobenius liftability II: surfaces and Fano threefolds

Piotr Achinger; Jakub Witaszek; Maciej Zdanowicz

doi:10.2422/2036-2145.202005_003

Global Frobenius liftability II: surfaces and Fano threefolds

Piotr Achinger
, Jakub Witaszek
, Maciej Zdanowicz

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this article, a sequel to Global Frobenius liftability I, we continue the development of a comprehensive theory of Frobenius liftings modulo p². We study compatibility of divisors and closed subschemes with Frobenius liftings, Frobenius liftings of blow-ups, descent under quotients by some group actions, stability under base change, and the properties of associated F -splittings. Consequently, we characterise Frobenius liftable surfaces and Fano threefolds in large characteristic, confirming the conjecture stated in our previous paper.

Original language	English (US)
Pages (from-to)	329-366
Number of pages	38
Journal	Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Volume	24
Issue number	1
DOIs	https://doi.org/10.2422/2036-2145.202005_003
State	Published - 2023

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Mathematics (miscellaneous)

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AU - Witaszek, Jakub

AU - Zdanowicz, Maciej

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Y1 - 2023

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AB - In this article, a sequel to Global Frobenius liftability I, we continue the development of a comprehensive theory of Frobenius liftings modulo p2. We study compatibility of divisors and closed subschemes with Frobenius liftings, Frobenius liftings of blow-ups, descent under quotients by some group actions, stability under base change, and the properties of associated F -splittings. Consequently, we characterise Frobenius liftable surfaces and Fano threefolds in large characteristic, confirming the conjecture stated in our previous paper.

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ER -

Global Frobenius liftability II: surfaces and Fano threefolds

Abstract

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