The Arinkin-Gaitsgory temperedness conjecture
Abstract
Arinkin and Gaitsgory defined a category of tempered D-modules on BunG that is conjecturally equivalent to the category of quasi-coherent (not ind-coherent!) sheaves on LocSysG. 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.
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