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arXiv · 1610.09323

On $(p,r)$-Filtrations and Tilting Modules

Paul Sobaje
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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. 2016-10-28. On $(p,r)$-Filtrations and Tilting Modules. https://arxiv.org/abs/1610.09323

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