Affiliation:
1. Department of Mathematics The University of Texas at Austin Austin Texas USA
Abstract
AbstractArinkin and Gaitsgory defined a category of tempered ‐modules on that is conjecturally equivalent to the category of quasi‐coherent (not ind‐coherent!) sheaves on . 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.
Funder
National Science Foundation
Reference23 articles.
1. Singular support of coherent sheaves and the geometric Langlands conjecture
2. D.Arinkin D.Gaitsgory D.Kazhdan S.Raskin N.Rozenblyum andY.Varshavsky The stack of local systems with restricted variation and geometric Langlands theory with nilpotent singular support arXiv preprint arXiv:2010.01906 2020.
3. D.Arinkin D.Gaitsgory D.Kazhdan S. R. N.Rozenblyum andY.Varshavsky Automorphic functions as the trace of Frobenius arXiv preprint arXiv:2102.07906 2021.
4. D.Ben‐ZviandD.Nadler Betti geometric Langlands Proceedings of Symposia in Pure Mathematics vol.97 2018 pp.3–41.
5. Sheaves of categories with local actions of Hochschild cochains