Coherent sheaves and quantum Coulomb branches I: tilting bundles from integrable systems

Abstract: In this paper, we consider how the approach of Bezrukavnikov and Kaledin to understanding the categories of coherent sheaves on symplectic resolutions can be applied to the Coulomb branches introduced by Braverman, Finkelberg and Nakajima. In particular, we construct tilting generators on resolved Coulomb branches, and give explicit quiver presentations of categories of coherent sheaves on these varieties, with the wall-crossing functors described by natural bimodules.