The strengthened Brou\'{e} abelian defect group conjecture for ${\rm SL}(2,p^n)$ and ${\rm GL}(2,p^n)$

Xin Huang; Pengcheng Li; Jiping Zhang

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arXiv · 2111.11145

The strengthened Brou\'{e} abelian defect group conjecture for ${\rm SL}(2,p^n)$ and ${\rm GL}(2,p^n)$

Xin Huang·Pengcheng Li·Jiping Zhang

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Abstract

We show that each $p$-block of ${\rm SL}(2,p^n)$ and ${\rm GL}(2,p^n)$ over an arbitrary complete discrete valuation ring is splendidly Rickard equivalent to its Brauer correspondent, hence give new evidence for a refined version of Brou\'{e}'s abelian defect group conjecture proposed by Kessar and Linckelmann.

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Xin Huang, Pengcheng Li, Jiping Zhang. 2021-11-22. The strengthened Brou\'{e} abelian defect group conjecture for ${\rm SL}(2,p^n)$ and ${\rm GL}(2,p^n)$. https://arxiv.org/abs/2111.11145

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