Extensions of vector bundles on the Fargues-Fontaine curve

Birkbeck, Christopher ORCID: https://orcid.org/0000-0002-7546-9028, Feng, Tony, Hansen, David, Hong, Serin, Li, Qirui, Wang, Anthony and Ye, Lynnelle (2022) Extensions of vector bundles on the Fargues-Fontaine curve. Journal of the Institute of Mathematics of Jussieu, 21 (2). pp. 487-532. ISSN 1474-7480

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Abstract

We completely classify the possible extensions between semistable vector bundles on the Fargues-Fontaine curve (over an algebraically closed perfectoid field), in terms of a simple condition on Harder-Narasimhan (HN) polygons. Our arguments rely on a careful study of various moduli spaces of bundle maps, which we define and analyze using Scholze's language of diamonds. This analysis reduces our main results to a somewhat involved combinatorial problem, which we then solve via a reinterpretation in terms of the Euclidean geometry of HN polygons.

Item Type: Article
Additional Information: Acknowledgements: The authors came together around these questions at the 2017 Arizona Winter School, under the umbrella of Kiran Kedlaya's project group. The authors would like to heartily thank Kiran for giving them this opportunity. They would also like to thank the organizers of the Winter School for creating such a wonderful experience, and they gratefully acknowledge NSF support of the Winter School via grant DMS-1504537.
Uncontrolled Keywords: diamonds,fargues-fontaine,vector bundles,mathematics(all) ,/dk/atira/pure/subjectarea/asjc/2600
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Algebra and Combinatorics
Related URLs:
Depositing User: LivePure Connector
Date Deposited: 15 May 2023 09:30
Last Modified: 14 Jul 2024 06:34
URI: https://ueaeprints.uea.ac.uk/id/eprint/92057
DOI: 10.1017/S1474748020000183

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