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The mod-$p$ Riemann–Hilbert correspondence and the perfect site

Akhil Mathew

Vol. 5 (2023), No. 2, 369–403
Abstract

The mod-p Riemann–Hilbert correspondence (in covariant and contravariant forms) relates 𝔽p-étale sheaves on the spectrum of an 𝔽p-algebra R and Frobenius modules over R. We give an exposition of these correspondences using Breen’s vanishing results on the perfect site.

Keywords
perfect site, mod p Riemann–Hilbert correspondence, étale sheaves
Mathematical Subject Classification
Primary: 14F08, 14F10, 14F20, 14F30
Milestones
Received: 22 June 2022
Revised: 23 October 2022
Accepted: 12 November 2022
Published: 4 June 2023
Authors
Akhil Mathew
Department of Mathematics
University of Chicago
IL
United States