The six functors for Zariski-constructible sheaves in rigid geometry. Issue 2 (26th February 2022)

• Record Type: Journal Article
• Authors: Bhatt, Bhargav; Hansen, David
• Is Part Of: Compositio mathematica. Volume 158:Issue 2(2022)
• Page Start: 437
• Page End: 482
• Publication Date: 2022-02-26
• Subjects: rigid analytic spaces -- étale cohomology -- generic smoothness -- six functors; 14G22 -- 14F20; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X22007291
• Languages: English
• ISSNs: 0010-437X

Abstract

Abstract : We prove a generic smoothness result in rigid analytic geometry over a characteristic zero non-archimedean field. The proof relies on a novel notion of generic points in rigid analytic geometry which are well adapted to 'spreading out' arguments, in analogy with the use of generic points in scheme theory. As an application, we develop a six-functor formalism for Zariski-constructible étale sheaves on characteristic zero rigid spaces. Among other things, this implies that characteristic zero rigid spaces support a well-behaved theory of perverse sheaves.