The strengthened Broué abelian defect group conjecture for $\mathrm{SL}(2,p^n)$ and $\mathrm{GL}(2,p^n)$

Abstract

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

arXiv commentrevised according to referee's comments, to appear in J. Algebra

References in corpus (1)

• Descent of equivalences for blocks with Klein four defect groups