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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On $(p,r)$-filtrations and tilting modules
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by Paul Sobaje PDF
Proc. Amer. Math. Soc. 146 (2018), 1951-1961 Request permission

Abstract:

We study the relationship between Donkin’s Tilting Module Conjecture and Donkin’s Good $(p,r)$-Filtration Conjecture. Our main result was motivated by a result of Kildetoft and Nakano showing that the Tilting Module Conjecture implies one direction of the Good $(p,r)$-Filtration Conjecture. We observe that the converse nearly holds; in particular, a weaker version of the Good $(p,r)$-Filtration Conjecture implies the Tilting Module Conjecture.
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Additional Information
  • Paul Sobaje
  • Affiliation: Department of Mathematics , University of Georgia , Athens, Georgia 30602
  • MR Author ID: 983585
  • Email: sobaje@uga.edu
  • Received by editor(s): December 21, 2016
  • Received by editor(s) in revised form: July 21, 2017
  • Published electronically: December 18, 2017
  • Additional Notes: This work was partially supported by the Research Training Grant, DMS-1344994, from the NSF
  • Communicated by: Pham Huu Tiep
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 146 (2018), 1951-1961
  • MSC (2010): Primary 20G05, 17B10
  • DOI: https://doi.org/10.1090/proc/13926
  • MathSciNet review: 3767348