Integral Artin motives II: Perverse motives and Artin Vanishing Theorem

Abstract

In this text, we are mainly interested in the existence of the perverse motivic t-structures on the category of Artin étale motives with integral coefficients. We construct the perverse homotopy t-structure which is the best possible approximation to a perverse t-structure on Artin motives with rational coefficients. The heart of this t-structure has properties similar to those of the category of perverse sheaves and contains the Ayoub-Zucker motive. With integral coefficients, we construct the perverse motivic t-structure on Artin motives when the base scheme is of dimension at most $2$ and show that it cannot exist in dimension $4$. This construction relies notably on a an analogue for Artin motives of the Artin Vanishing Theorem.

60 pages, comments welcome. arXiv:2211.02505 was split in two parts and this paper is the second part. This is the published version of part II, the plan was changed completely. Some material was removed (e.g. section 4.4) but is correct and can be used elsewhere if needed