Cotangent bundle and microsupports in the mixed characteristic case

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 micro-supported on a closed conical subset in the FW-cotangent bundle. At the end of the article, we compute the singular supports in some cases.