On $(p,r)$-filtrations and tilting modules
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Abstract:
We study the relationship between Donkinβs Tilting Module Conjecture and Donkinβs 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.References
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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