Cotangent bundle and micro-supports in 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 etale 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.

30 pages. In v4, in the construction of the cotangent bundle, the cotangent complex is replaced by the sheaf of FW-differentials, introduced in the article arXiv:2008.04728. Accordingly, the part studying cotangent complexes is moved to the other article. The order of the sections 1 and 2 are switched

References in corpus (3)

• The characteristic cycle and the singular support of a constructible sheaf
• Frobenius-Witt differentials and regularity
• Graded quotients of ramification groups of local fields with imperfect residue fields

Cited by in corpus (2)

• Frobenius-Witt differentials and regularity
• Cohomological Milnor formula and Saito's conjecture on characteristic classes