Vol. 3, No. 4, 2021

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Moduli of local shtukas and Harris's conjecture

David Hansen

Vol. 3 (2021), No. 4, 749–799
Abstract

We prove, under a certain assumption of “Hodge–Newton reducibility”, a strong form of a conjecture of Harris on the cohomology of moduli spaces of mixed-characteristic local shtukas for GLn. Our strategy is roughly based on a previous strategy developed by Mantovan in the setting of p-divisible groups, but the arguments are completely different. In particular, we reinterpret and generalize the Hodge–Newton filtration of a p-divisible group in terms of modified vector bundles on the Fargues–Fontaine curve. We also compute the dualizing complex and compactly supported étale cohomology of any positive Banach–Colmez space over any base; this should be of independent interest.

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Keywords
local shtukas, Harris's conjecture, perfectoid spaces, diamonds
Mathematical Subject Classification
Primary: 11S37, 14G22, 14G45
Milestones
Received: 13 July 2020
Accepted: 22 March 2021
Published: 20 October 2021
Authors
David Hansen
Max Planck Institute for Mathematics
Bonn
Germany