Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 10, 1681–1865
Issue 9, 1533–1680
Issue 8, 1359–1532
Issue 7, 1239–1357
Issue 6, 1127–1237
Issue 5, 981–1126
Issue 4, 805–980
Issue 3, 541–804
Issue 2, 267–539
Issue 1, 1–266

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
The local Langlands correspondence for $\mathrm{GL}_n$ over function fields

Siyan Daniel Li-Huerta

Vol. 16 (2022), No. 9, 2119–2214
Abstract

Let F be a local field of characteristic p > 0. By adapting methods of Scholze (2013), we give a new proof of the local Langlands correspondence for GL n over F. More specifically, we construct -adic Galois representations associated with many discrete automorphic representations over global function fields, which we use to construct a map πrec (π) from isomorphism classes of irreducible smooth representations of GL n(F) to isomorphism classes of n-dimensional semisimple continuous representations of WF. Our map rec is characterized in terms of a local compatibility condition on traces of a certain test function fτ,h, and we prove that rec equals the usual local Langlands correspondence (after forgetting the monodromy operator).

Keywords
local Langlands correspondence, function fields, D-elliptic sheaves
Mathematical Subject Classification
Primary: 11F70, 11S37
Secondary: 11G09
Milestones
Received: 12 March 2021
Revised: 7 November 2021
Accepted: 3 January 2022
Published: 19 December 2022
Authors
Siyan Daniel Li-Huerta
Harvard University
Cambridge
MA
United States