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

Chenji Fu

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arXiv · 2504.13869

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

Chenji Fu

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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_{Z_l-bar}G(F) containing a depth-zero regular supercuspidal irreducible representation \pi over 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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Chenji Fu. 2025-03-29. On the categorical local Langlands conjectures for depth-zero regular supercuspidal representations. https://arxiv.org/abs/2504.13869

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