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On $ (p,r)$-filtrations and tilting modules


Author: Paul Sobaje
Journal: Proc. Amer. Math. Soc. 146 (2018), 1951-1961
MSC (2010): Primary 20G05, 17B10
DOI: https://doi.org/10.1090/proc/13926
Published electronically: December 18, 2017
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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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Paul Sobaje
Affiliation: Department of Mathematics University of Georgia Athens, Georgia 30602
Email: sobaje@uga.edu

DOI: https://doi.org/10.1090/proc/13926
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
Article copyright: © Copyright 2017 American Mathematical Society

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