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Title: The six functors for Zariski-constructible sheaves in rigid geometry
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.  more » « less
Award ID(s):
1801689 1952399 1840234
Author(s) / Creator(s):
Date Published:
Journal Name:
Compositio Mathematica
Page Range / eLocation ID:
437 to 482
Medium: X
Sponsoring Org:
National Science Foundation
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