2021/06/09 by Siyan Daniel Li-Huerta, Li-Huerta, Siyan Daniel
Mathematics · #11G09 (Secondary) #11G18 (Primary) 22E57 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2106.05382
openalex publication_date 2021/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove the plectic conjecture of Nekovář-Scholl over global function fields Q. For example, when the cocharacter is defined over Q and the structure group is a Weil restriction from a geometric degree d separable extension F/Q, consider the complex computing ℓ-adic intersection cohomology with compact support of the associated moduli space of shtukas over QI. We endow this with the structure of a complex of \DeclareMathOperator\WeilWeil(\Weil(F)d\rtimes\mathfrakSd)I-modules, which extends its structure as a complex of \Weil(Q)I-modules constructed by Arinkin-Gaitsgory-Kazhdan-Raskin-Rozenblyum-Varshavsky. We show that the action of (\Weil(F)d\rtimes\mathfrakSd)I commutes with the Hecke action, and we give a moduli-theoretic description of the action of Frobenius elements in \Weil(F)d× I.