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Nilpotence order growth
of recursion operators in characteristic $p$
Anna Medvedovsky |
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Vol. 12 (2018), No. 3, 693–722
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Abstract |
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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 Hecke algebra in the genus-zero case. We sketch the application for and in level one. The case was first established in by Nicolas and Serre in 2012 using different methods. |
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Keywords
linear recurrences in characteristic $p$, modular forms
modulo $p$, congruences between modular forms, $ \bmod p$
Hecke algebras, $p$-regular sequences, base representation
of numbers
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Mathematical Subject Classification 2010
Primary: 11T55
Secondary: 11B85, 11F03, 11F33
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Milestones
Received: 27 July 2017
Revised: 12 January 2018
Accepted: 23 February 2018
Published: 12 June 2018
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Authors |
| Anna Medvedovsky | |
| Max-Planck-Institut für
Mathematik Bonn Germany |
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