Derived non-archimedean analytic spaces
- Creators
- Porta, Mauro
- Yu, Tony Yue
Abstract
We propose a derived version of non-archimedean analytic geometry. Intuitively, a derived non-archimedean analytic space consists of an ordinary non-archimedean analytic space equipped with a sheaf of derived rings. Such a naive definition turns out to be insufficient. In this paper, we resort to the theory of pregeometries and structured topoi introduced by Jacob Lurie. We prove the following three fundamental properties of derived non-archimedean analytic spaces: (1) The category of ordinary non-archimedean analytic spaces embeds fully faithfully into the ∞-category of derived non-archimedean analytic spaces. (2) The ∞-category of derived non-archimedean analytic spaces admits fiber products. (3) The ∞-category of higher non-archimedean analytic Deligne–Mumford stacks embeds fully faithfully into the ∞-category of derived non-archimedean analytic spaces. The essential image of this embedding is spanned by n-localic discrete derived non-archimedean analytic spaces. We will further develop the theory of derived non-archimedean analytic geometry in our subsequent works. Our motivations mainly come from intersection theory, enumerative geometry and mirror symmetry.
Additional Information
© 2018 Springer. Published 09 February 2017. Issue Date: April 2018. We are grateful to Vladimir Berkovich, Antoine Chambert-Loir, Brian Conrad, Antoine Ducros, Bruno Klingler, Maxim Kontsevich, Jacob Lurie, Marco Robalo, Matthieu Romagny, Pierre Schapira, Carlos Simpson, Michael Temkin, Bertrand Toën and Gabriele Vezzosi for valuable discussions. The authors would also like to thank each other for the joint effort. This research was partially conducted during the period Mauro Porta was supported by Simons Foundation grant number 347070 and the group GNSAGA, and Tony Yue Yu served as a Clay Research Fellow.Attached Files
Submitted - 1601.00859.pdf
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Additional details
- Eprint ID
- 110830
- Resolver ID
- CaltechAUTHORS:20210914-164412737
- 347070
- Simons Foundation
- Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni (GNSAGA)
- Clay Mathematics Institute
- Created
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2021-09-14Created from EPrint's datestamp field
- Updated
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2021-09-14Created from EPrint's last_modified field