Mod-$2$ Hecke algebras of level $3$ and $5$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866929604317413376 |
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| author | Deo, Shaunak V. Medvedovsky, Anna |
| author_facet | Deo, Shaunak V. Medvedovsky, Anna |
| contents | We use deformation theory to study the big Hecke algebra acting on mod-2 modular forms of prime level $N$ and all weights, especially its local component at the trivial representation. For $N = 3, 5$, we prove that the maximal reduced quotient of this big Hecke algebra is isomorphic to the maximal reduced quotient of the corresponding universal deformation ring. Then we completely determine the structure of this big Hecke algebra. We also describe a natural grading on mod-$p$ Hecke algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_00429 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Mod-$2$ Hecke algebras of level $3$ and $5$ Deo, Shaunak V. Medvedovsky, Anna Number Theory 11F25, 11F33, 11F80 (primary), 20C08 We use deformation theory to study the big Hecke algebra acting on mod-2 modular forms of prime level $N$ and all weights, especially its local component at the trivial representation. For $N = 3, 5$, we prove that the maximal reduced quotient of this big Hecke algebra is isomorphic to the maximal reduced quotient of the corresponding universal deformation ring. Then we completely determine the structure of this big Hecke algebra. We also describe a natural grading on mod-$p$ Hecke algebras. |
| title | Mod-$2$ Hecke algebras of level $3$ and $5$ |
| topic | Number Theory 11F25, 11F33, 11F80 (primary), 20C08 |
| url | https://arxiv.org/abs/2208.00429 |