A Brauer--Galois height zero conjecture Article Swipe

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Gunter Malle , Alexander Moretó , Noelia Rizo , A. A. Schaeffer Fry ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2402.08361

Recently, Malle and Navarro obtained a Galois strengthening of Brauer's height zero conjecture for principal $p$-blocks when $p=2$, considering a particular Galois automorphism of order~$2$. In this paper, for any prime $p$ we consider a certain elementary abelian $p$-subgroup of the absolute Galois group and propose a Galois version of Brauer's height zero conjecture for principal $p$-blocks. We prove it when $p=2$ and also for arbitrary $p$ when $G$ does not involve certain groups of Lie type of small rank as composition factors. Furthermore, we prove it for almost simple groups and for $p$-solvable groups.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2402.08361
PDF: https://arxiv.org/pdf/2402.08361
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4391833759

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DOI: https://doi.org/10.48550/arxiv.2402.08361

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Title: A Brauer--Galois height zero conjecture

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Language: en

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Publication year: 2024

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Publication date: 2024-02-13

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Authors: Gunter Malle, Alexander Moretó, Noelia Rizo, A. A. Schaeffer Fry

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Landing page: https://arxiv.org/abs/2402.08361

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Concepts: Zero (linguistics), Mathematics, Conjecture, Galois group, Galois module, Pure mathematics, Linguistics, Philosophy

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