A toy model for the Drinfeld–Lafforgue shtuka construction

D. Gaitsgory; D. Kazhdan; N. Rozenblyum; Y. Varshavsky

doi:10.1016/j.indag.2021.11.002

A toy model for the Drinfeld–Lafforgue shtuka construction

D. Gaitsgory^*, D. Kazhdan, N. Rozenblyum, Y. Varshavsky

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The goal of this paper is to provide a categorical framework that leads to the definition of shtukas à la Drinfeld and of excursion operators à la V. Lafforgue. We take as the point of departure the Hecke action of Rep(Gˇ) on the category Shv(Bun_G) of sheaves on Bun_G, and also the endofunctor of the latter category, given by the action of the geometric Frobenius. The shtuka construction will be obtained by applying (various versions of) categorical trace.

Original language	English
Pages (from-to)	39-189
Number of pages	151
Journal	Indagationes Mathematicae
Volume	33
Issue number	1
DOIs	https://doi.org/10.1016/j.indag.2021.11.002
State	Published - Jan 2022

Bibliographical note

Publisher Copyright:
© 2021 Royal Dutch Mathematical Society (KWG)

Keywords

Geometric Langlands
Shtuka
Trace

Access to Document

10.1016/j.indag.2021.11.002

Cite this

@article{76bad90255464f9999f417b7c5478e0e,

title = "A toy model for the Drinfeld–Lafforgue shtuka construction",

abstract = "The goal of this paper is to provide a categorical framework that leads to the definition of shtukas {\`a} la Drinfeld and of excursion operators {\`a} la V. Lafforgue. We take as the point of departure the Hecke action of Rep(Gˇ) on the category Shv(BunG) of sheaves on BunG, and also the endofunctor of the latter category, given by the action of the geometric Frobenius. The shtuka construction will be obtained by applying (various versions of) categorical trace.",

keywords = "Geometric Langlands, Shtuka, Trace",

author = "D. Gaitsgory and D. Kazhdan and N. Rozenblyum and Y. Varshavsky",

note = "Publisher Copyright: {\textcopyright} 2021 Royal Dutch Mathematical Society (KWG)",

year = "2022",

month = jan,

doi = "10.1016/j.indag.2021.11.002",

language = "אנגלית",

volume = "33",

pages = "39--189",

journal = "Indagationes Mathematicae",

issn = "0019-3577",

publisher = "Elsevier",

number = "1",

}

TY - JOUR

T1 - A toy model for the Drinfeld–Lafforgue shtuka construction

AU - Gaitsgory, D.

AU - Kazhdan, D.

AU - Rozenblyum, N.

AU - Varshavsky, Y.

PY - 2022/1

Y1 - 2022/1

N2 - The goal of this paper is to provide a categorical framework that leads to the definition of shtukas à la Drinfeld and of excursion operators à la V. Lafforgue. We take as the point of departure the Hecke action of Rep(Gˇ) on the category Shv(BunG) of sheaves on BunG, and also the endofunctor of the latter category, given by the action of the geometric Frobenius. The shtuka construction will be obtained by applying (various versions of) categorical trace.

AB - The goal of this paper is to provide a categorical framework that leads to the definition of shtukas à la Drinfeld and of excursion operators à la V. Lafforgue. We take as the point of departure the Hecke action of Rep(Gˇ) on the category Shv(BunG) of sheaves on BunG, and also the endofunctor of the latter category, given by the action of the geometric Frobenius. The shtuka construction will be obtained by applying (various versions of) categorical trace.

KW - Geometric Langlands

KW - Shtuka

KW - Trace

UR - http://www.scopus.com/inward/record.url?scp=85121529133&partnerID=8YFLogxK

U2 - 10.1016/j.indag.2021.11.002

DO - 10.1016/j.indag.2021.11.002

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85121529133

SN - 0019-3577

VL - 33

SP - 39

EP - 189

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 1

ER -

A toy model for the Drinfeld–Lafforgue shtuka construction

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this