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arXiv · 1901.06687

Counterexamples to the Tilting and $(p,r)$-Filtration Conjectures

Christopher P. Bendel·Daniel K. Nakano·Cornelius Pillen·Paul Sobaje
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Abstract

In this paper the authors produce a projective indecomposable module for the Frobenius kernel of a simple algebraic group in characteristic $p$ that is not the restriction of an indecomposable tilting module. This yields a counterexample to Donkin's longstanding Tilting Module Conjecture. The authors also produce a Weyl module that does not admit a $p$-Weyl filtration. This answers an old question of Jantzen, and also provides a counterexample to the $(p,r)$-Filtration Conjecture.

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BibTeXRIS

Christopher P. Bendel, Daniel K. Nakano, Cornelius Pillen, Paul Sobaje. 2019-01-20. Counterexamples to the Tilting and $(p,r)$-Filtration Conjectures. https://arxiv.org/abs/1901.06687

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