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.

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