On (p, r)-filtrations and tilting modules

Paul Sobaje

doi:10.1090/proc/13926

On (p, r)-filtrations and tilting modules

Paul Sobaje

Mathematical Sciences

University of Georgia

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English
Pages (from-to)	1951-1961
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	146
Issue number	5
DOIs	https://doi.org/10.1090/proc/13926
State	Published - Jan 1 2018

Scopus Subject Areas

General Mathematics
Applied Mathematics

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Cite this

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abstract = "We study the relationship between Donkin{\textquoteright}s Tilting Module Conjecture and Donkin{\textquoteright}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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AB - 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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On (p, r)-filtrations and tilting modules

Abstract

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