The stack of local systems and ind-coherent sheaves
Hot Topics: Geometric Langlands Conjecture April 06, 2026 - April 10, 2026
Location: SLMath: Eisenbud Auditorium, Online/Virtual
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The stack of local systems and ind-coherent sheaves
The goal of this talk is to formalize the spectral side of the geometric Langlands equivalence. We define the stack LocSys of de Rham local systems and prove its basic properties. Beilinson and Drinfeld's "best hope" for the geometric Langlands equivalence uses quasi-coherent sheaves on LocSys, but that category is too small for the equivalence. We therefore enlarge QCoh(LocSys) to the category of ind-coherent sheaves on LocSys with nilpotent singular support.
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The stack of local systems and ind-coherent sheaves
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