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The six functors for Zariski-constructible sheaves in rigid geometry

Compositio mathematica, 2022-02, Vol.158 (2), p.437-482 [Peer Reviewed Journal]

2022 The Author(s) ;2022 The Author(s). This work is licensed under the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0 (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. ;ISSN: 0010-437X ;EISSN: 1570-5846 ;DOI: 10.1112/S0010437X22007291

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  • Title:
    The six functors for Zariski-constructible sheaves in rigid geometry
  • Author: Bhatt, Bhargav ; Hansen, David
  • Subjects: Algebra ; Analytic geometry ; Geometry ; Sheaves ; Smoothness ; Theorems
  • Is Part Of: Compositio mathematica, 2022-02, Vol.158 (2), p.437-482
  • Description: 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.
  • Publisher: London, UK: London Mathematical Society
  • Language: English;French
  • Identifier: ISSN: 0010-437X
    EISSN: 1570-5846
    DOI: 10.1112/S0010437X22007291
  • Source: ProQuest Central
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