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

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	American 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

Funding Information:
Part of the project was carried out while D.G, N.R and Y.V were at MSRI and were supported by NSF grant DMS-1440140 .

Funding Information:
The project has received funding from ERC under Grant Agreement No. 669655 .

Funding Information:
The research of D.G. was supported by NSF grant DMS-1707662 and by Gelfand Chair at IHES. The research of Y.V. was supported by the ISF grant 822/17.Part of the project was carried out while D.G, N.R and Y.V were at MSRI and were supported by NSF grant DMS-1440140.The project has received funding from ERC under Grant Agreement No. 669655.

Funding Information:
The research of D.G. was supported by NSF grant DMS-1707662 and by Gelfand Chair at IHES . The research of Y.V. was supported by the ISF grant 822/17 .

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

Keywords

Geometric Langlands
Shtuka
Trace

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10.1016/j.indag.2021.11.002

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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",

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A toy model for the Drinfeld–Lafforgue shtuka construction

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Keywords

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