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

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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microsupport, singular support, mixed characteristic, transversality, Frobenius–Witt differentials, cotangent bundle
Mathematical Subject Classification
Primary: 14F20
Received: 30 May 2020
Revised: 1 February 2021
Accepted: 7 July 2021
Published: 27 April 2022
Takeshi Saito
School of Mathematical Sciences
University of Tokyo