Hecke correspondences for smooth moduli spaces of sheaves

Andrei Neguţ

doi:10.1007/s10240-022-00131-1

Article

Hecke correspondences for smooth moduli spaces of sheaves

Andrei Neguţ ¹

¹

Publications Mathématiques de l'IHÉS, Volume 135 (2022), pp. 337-418

Abstract

We define functors on the derived category of the moduli space ℳ of stable sheaves on a smooth projective surface (under Assumptions A and S below), and prove that these functors satisfy certain commutation relations. These relations allow us to prove that the given functors induce an action of the elliptic Hall algebra on the $K$ -theory of the moduli space ℳ, thus generalizing the action studied by Nakajima, Grojnowski and Baranovsky in cohomology.

Received: 2020-04-29
Accepted: 2022-05-06
Online First: 2022-05-11
Published online: 2022-06-07

Zbl

DOI: 10.1007/s10240-022-00131-1

Author's affiliations:

Andrei Neguţ ¹

¹

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     author = {Andrei Negu\c{t}},
     title = {Hecke correspondences for smooth moduli spaces of sheaves},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {337--418},
     year = {2022},
     publisher = {Springer International Publishing},
     address = {Cham},
     volume = {135},
     doi = {10.1007/s10240-022-00131-1},
     zbl = {1506.14029},
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Andrei Neguţ. Hecke correspondences for smooth moduli spaces of sheaves. Publications Mathématiques de l'IHÉS, Volume 135 (2022), pp. 337-418. doi: 10.1007/s10240-022-00131-1

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