Vol. 12, No. 3, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 15
Issue 6, 1343–1592
Issue 5, 1077–1342
Issue 4, 821–1076
Issue 3, 569–820
Issue 2, 309–567
Issue 1, 1–308

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
Nilpotence order growth of recursion operators in characteristic $p$

Anna Medvedovsky

Vol. 12 (2018), No. 3, 693–722
Abstract

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.

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
Mathematical Subject Classification 2010
Primary: 11T55
Secondary: 11B85, 11F03, 11F33
Milestones
Received: 27 July 2017
Revised: 12 January 2018
Accepted: 23 February 2018
Published: 12 June 2018
Authors
Anna Medvedovsky
Max-Planck-Institut für Mathematik
Bonn
Germany