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Winter 2020 Frobenius split subvarieties pull back in almost all characteristics
David E Speyer
J. Commut. Algebra 12(4): 573-579 (Winter 2020). DOI: 10.1216/jca.2020.12.573

Abstract

Let 𝒳 and 𝒴 be schemes of finite type over Spec and let α:𝒴𝒳 be a finite map. We show the following holds for all sufficiently large primes p: If ϕ and ψ are any splittings on 𝒳× Spec𝔽p and 𝒴× Spec𝔽p, such that the restriction of α is compatible with ϕ and ψ, and V is any compatibly split subvariety of (𝒳× Spec𝔽p,ϕ), then the reduction α1(V)red is a compatibly split subvariety of (𝒴× Spec𝔽p,ψ). This is meant as a tool to aid in listing the compatibly split subvarieties of various classically split varieties.

Citation

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David E Speyer. "Frobenius split subvarieties pull back in almost all characteristics." J. Commut. Algebra 12 (4) 573 - 579, Winter 2020. https://doi.org/10.1216/jca.2020.12.573

Information

Received: 17 October 2016; Revised: 6 July 2017; Accepted: 24 February 2018; Published: Winter 2020
First available in Project Euclid: 5 January 2021

MathSciNet: MR4194942
Digital Object Identifier: 10.1216/jca.2020.12.573

Subjects:
Primary: 13A35

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.12 • No. 4 • Winter 2020
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