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This article is available for purchase or by subscription. See below.
Abstract
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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
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Our strategy is roughly based on a previous strategy developed by Mantovan in the setting
of
-divisible
groups, but the arguments are completely different. In particular,
we reinterpret and generalize the Hodge–Newton filtration of a
-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
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Mathematical Subject Classification
Primary: 11S37, 14G22, 14G45
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Milestones
Received: 13 July 2020
Accepted: 22 March 2021
Published: 20 October 2021
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