An Iwahori theoretic mod $p$ Local Langlands Correspondence
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908525846855680 |
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| author | Chitrao, Anand |
| author_facet | Chitrao, Anand |
| contents | We extend a comparison theorem of Anandavardhanan-Borisagar between the quotient of the induction of a mod $p$ character by the image of an Iwahori-Hecke operator and compact induction of a weight to the case of the trivial character. This involves studying the corresponding non-commutative Iwahori-Hecke algebra. We use this to give an Iwahori theoretic reformulation of the (semi-simple) mod $p$ Local Langlands Correspondence discovered by Breuil and reformulated functorially by Colmez. This version of the correspondence is expected to have applications to computing the mod $p$ reductions of semi-stable Galois representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_02919 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An Iwahori theoretic mod $p$ Local Langlands Correspondence Chitrao, Anand Number Theory Representation Theory We extend a comparison theorem of Anandavardhanan-Borisagar between the quotient of the induction of a mod $p$ character by the image of an Iwahori-Hecke operator and compact induction of a weight to the case of the trivial character. This involves studying the corresponding non-commutative Iwahori-Hecke algebra. We use this to give an Iwahori theoretic reformulation of the (semi-simple) mod $p$ Local Langlands Correspondence discovered by Breuil and reformulated functorially by Colmez. This version of the correspondence is expected to have applications to computing the mod $p$ reductions of semi-stable Galois representations. |
| title | An Iwahori theoretic mod $p$ Local Langlands Correspondence |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2311.02919 |