On the categorical local Langlands conjectures for depth-zero regular supercuspidal representations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910914277539840 |
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| author | Fu, Chenji |
| author_facet | Fu, Chenji |
| contents | 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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13869 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the categorical local Langlands conjectures for depth-zero regular supercuspidal representations Fu, Chenji Representation Theory Algebraic Geometry Number Theory 11S37, 22E57, 22E50 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 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. |
| title | On the categorical local Langlands conjectures for depth-zero regular supercuspidal representations |
| topic | Representation Theory Algebraic Geometry Number Theory 11S37, 22E57, 22E50 |
| url | https://arxiv.org/abs/2504.13869 |