On the categorical local Langlands conjectures for depth-zero regular supercuspidal representations

2025/03/29 by Fu, Chenji
#11S37 #22E50 #22E57 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2504.13869

Abstract

Let F be a non-archimedean local field with residue characteristic p. Let l be a prime number different from p. Let G be a connected reductive group which is split, semi-simple, and simply connected. On the one hand, we describe the category of quasi-coherent sheaves on the connected component of the stack of L-parameters over Z_l-bar containing a tame, regular semisimple, elliptic L-parameter over F_l-bar. On the other hand, we describe the block of Rep_Zl-barG(F) containing a depth-zero regular supercuspidal irreducible representation πover F_l-bar. For G=GL_n, we compute both sides explicitly and verify the categorical local Langlands conjecture for depth-zero supercuspidal blocks.

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