The Arinkin-Gaitsgory temperedness conjecture
Algebraic Geometry
2021-08-06 v1 Representation Theory
Abstract
Arinkin and Gaitsgory defined a category of tempered D-modules on Bun_G that is conjecturally equivalent to the category of quasi-coherent (not ind-coherent!) sheaves on LocSys_{\check{G}}. However, their definition depends on the auxiliary data of a point of the curve; they conjectured that their definition is independent of this choice. Beraldo has outlined a proof of this conjecture that depends on some technology that is not currently available. Here we provide a short, unconditional proof of the Arinkin-Gaitsgory conjecture.
Keywords
Cite
@article{arxiv.2108.02719,
title = {The Arinkin-Gaitsgory temperedness conjecture},
author = {Joakim Faergeman and Sam Raskin},
journal= {arXiv preprint arXiv:2108.02719},
year = {2021}
}