Cotangent bundle and microsupports in the mixed characteristic case

Saito, Takeshi

doi:10.2140/ant.2022.16.335

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Cotangent bundle and microsupports in the mixed characteristic case

Takeshi Saito

Vol. 16 (2022), No. 2, 335–368

DOI: 10.2140/ant.2022.16.335

Abstract

For a regular scheme and a prime number $p$ , we define the FW-cotangent bundle as a vector bundle on the closed subscheme defined by $p = 0$ , under a certain finiteness condition.

For a constructible complex on the étale site of the scheme, we introduce the condition to be microsupported on a closed conical subset in the FW-cotangent bundle. At the end of the article, we compute the singular supports in some cases.

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Keywords

microsupport, singular support, mixed characteristic, transversality, Frobenius–Witt differentials, cotangent bundle

Mathematical Subject Classification

Primary: 14F20

Milestones

Received: 30 May 2020

Revised: 1 February 2021

Accepted: 7 July 2021

Published: 27 April 2022

Authors

Takeshi Saito
School of Mathematical Sciences University of Tokyo Japan

Vol. 16, No. 2, 2022