Vol. 16, No. 2, 2022

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Cotangent bundle and microsupports in the mixed characteristic case

Takeshi Saito

Vol. 16 (2022), No. 2, 335–368
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