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2019 Purity of crystalline strata
Jinghao Li, Adrian Vasiu
Tunisian J. Math. 1(4): 519-538 (2019). DOI: 10.2140/tunis.2019.1.519

Abstract

Let p be a prime. Let n. Let C be an Fn-crystal over a locally noetherian Fp-scheme S. Let (a,b)2. We show that the reduced locally closed subscheme of S whose points are exactly those xS such that (a,b) is a break point of the Newton polygon of the fiber Cx of C at x is pure in S, i.e., it is an affine S-scheme. This result refines and reobtains previous results of de Jong and Oort, of Vasiu, and of Yang. As an application, we show that for all m the reduced locally closed subscheme of S whose points are exactly those xS for which the p-rank of Cx is m is pure in S; the case n=1 was previously obtained by Deligne (unpublished) and the general case n1 refines and reobtains a result of Zink.

Citation

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Jinghao Li. Adrian Vasiu. "Purity of crystalline strata." Tunisian J. Math. 1 (4) 519 - 538, 2019. https://doi.org/10.2140/tunis.2019.1.519

Information

Received: 28 January 2018; Revised: 8 August 2018; Accepted: 5 September 2018; Published: 2019
First available in Project Euclid: 18 December 2018

zbMATH: 07027464
MathSciNet: MR3892250
Digital Object Identifier: 10.2140/tunis.2019.1.519

Subjects:
Primary: 11G18, 14F30, 14L05
Secondary: 11G10, 14G35, 14K10, 14K99, 14L15

Rights: Copyright © 2019 Mathematical Sciences Publishers

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