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| Format: | Preprint |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1707.09846 |
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| _version_ | 1866910714340311040 |
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| author | Medvedovsky, Anna |
| author_facet | Medvedovsky, Anna |
| contents | We prove that the killing rate of certain degree-lowering "recursion operators" on a polynomial algebra over a finite field grows slower than linearly in the degree of the polynomial attacked. We also explain the motivating application: obtaining a lower bound for the Krull dimension of a local component of a big mod-p Hecke algebra in the genus-zero case. We sketch the application for p=2 and p=3 in level one. The case p=2 was first established in by Nicolas and Serre in 2012 using different methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1707_09846 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Nilpotence order growth of recursion operators in characteristic p Medvedovsky, Anna Number Theory Rings and Algebras We prove that the killing rate of certain degree-lowering "recursion operators" on a polynomial algebra over a finite field grows slower than linearly in the degree of the polynomial attacked. We also explain the motivating application: obtaining a lower bound for the Krull dimension of a local component of a big mod-p Hecke algebra in the genus-zero case. We sketch the application for p=2 and p=3 in level one. The case p=2 was first established in by Nicolas and Serre in 2012 using different methods. |
| title | Nilpotence order growth of recursion operators in characteristic p |
| topic | Number Theory Rings and Algebras |
| url | https://arxiv.org/abs/1707.09846 |