Cotangent bundle and micro-supports in mixed characteristic case
Algebraic Geometry
2022-04-27 v7
Abstract
For a regular scheme and a prime number , we define the FW-cotangent bundle as a vector bundle on the closed subscheme defined by , 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.
Keywords
Cite
@article{arxiv.2006.00448,
title = {Cotangent bundle and micro-supports in mixed characteristic case},
author = {Takeshi Saito},
journal= {arXiv preprint arXiv:2006.00448},
year = {2022}
}
Comments
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