Porta, Mauro and Yu, Tony Yue (2016) Higher analytic stacks and GAGA theorems. Advances in Mathematics, 302 . pp. 351-409. ISSN 0001-8708. doi:10.1016/j.aim.2016.07.017. https://resolver.caltech.edu/CaltechAUTHORS:20210914-164412895
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Abstract
We develop the foundations of higher geometric stacks in complex analytic geometry and in non-archimedean analytic geometry. We study coherent sheaves and prove the analog of Grauert's theorem for derived direct images under proper morphisms. We define analytification functors and prove the analog of Serre's GAGA theorems for higher stacks. We use the language of infinity category to simplify the theory. In particular, it enables us to circumvent the functoriality problem of the lisse-étale sites for sheaves on stacks. Our constructions and theorems cover the classical 1-stacks as a special case.
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| Additional Information: | © 2016 Elsevier Under an Elsevier user license. Received 18 January 2015, Revised 6 July 2016, Accepted 18 July 2016, Available online 1 August 2016. We are grateful to Antoine Chambert-Loir, Antoine Ducros, Maxim Kontsevich, Yves Laszlo, Valerio Melani, François Petit, Marco Robalo, Matthieu Romagny, Pierre Schapira, Michael Temkin and Gabriele Vezzosi for very useful discussions. The authors would also like to thank each other for the joint effort. | |||||||||
| Subject Keywords: | Analytic stack; Higher stack; Grauert's theorem; Analytification; GAGA; Rigid analytic geometry; Berkovich space; Infinity category | |||||||||
| Classification Code: | MSC: primary 14A20; secondary 14G22, 32C35, 14F05 | |||||||||
| DOI: | 10.1016/j.aim.2016.07.017 | |||||||||
| Record Number: | CaltechAUTHORS:20210914-164412895 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20210914-164412895 | |||||||||
| Official Citation: | Mauro Porta, Tony Yue Yu, Higher analytic stacks and GAGA theorems, Advances in Mathematics, Volume 302, 2016, Pages 351-409, ISSN 0001-8708, https://doi.org/10.1016/j.aim.2016.07.017. | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 110832 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | George Porter | |||||||||
| Deposited On: | 14 Sep 2021 22:02 | |||||||||
| Last Modified: | 14 Sep 2021 22:11 |
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