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Derived Hom spaces in rigid analytic geometry

Porta, Mauro and Yu, Tony Yue (2018) Derived Hom spaces in rigid analytic geometry. . (Unpublished)

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We construct a derived enhancement of Hom spaces between rigid analytic spaces. It encodes the hidden deformation-theoretic informations of the underlying classical moduli space. The main tool in our construction is the representability theorem in derived analytic geometry, which has been established in our previous work. The representability theorem provides us sufficient and necessary conditions for an analytic moduli functor to possess the structure of a derived analytic stack. In order to verify the conditions of the representability theorem, we prove several general results in the context of derived non-archimedean analytic geometry: derived Tate acyclicity, projection formula, and proper base change. These results also deserve independent interest themselves. Our main motivation comes from non-archimedean enumerative geometry. In our subsequent works, we will apply the derived mapping stacks to obtain non-archimedean analytic Gromov-Witten invariants.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Porta, Mauro0000-0002-1239-3409
Yu, Tony Yue0000-0002-6019-8552
Additional Information:We are very grateful to Antoine Chambert-Loir, Maxim Kontsevich, Jacob Lurie, Tony Pantev, Marco Robalo, Carlos Simpson, Bertrand Toën and Gabriele Vezzosi for valuable discussions. The authors would also like to thank each other for the joint effort. Various stages of this research received supports from the Clay Mathematics Institute, Simons Foundation grant number 347070, and from the Ky Fan and Yu-Fen Fan Membership Fund and the S.-S. Chern Endowment Fund of the Institute for Advanced Study.
Funding AgencyGrant Number
Clay Mathematics InstituteUNSPECIFIED
Simons Foundation347070
Ky Fan and Yu-Fen Fan Membership FundUNSPECIFIED
Institute for Advanced StudyUNSPECIFIED
Subject Keywords:mapping stack, Hom scheme, representability, derived geometry, rigid analytic geometry, non-archimedean geometry, Tate acyclicity, projection formula, proper base change
Classification Code:2010 Mathematics Subject Classification. Primary 14G22; Secondary 14D23, 18G55.
Record Number:CaltechAUTHORS:20210914-164506886
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110837
Deposited By: George Porter
Deposited On:14 Sep 2021 17:41
Last Modified:02 Jun 2023 00:38

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