Catégories dérivées et variétés de Deligne-Lusztig

By C. Bonnafé, Raphaël Rouquier. 2002

113 citations recorded by the source corpus.

We prove a conjecture of Broue about the Jordan decomposition of blocks of finite reductive groups. We show that a block of a finite connected reductive group, in non-describing characteristic, is Morita-equivalent to a quasi-isolated block of a Levi subgroup. This involves showing that some local system over a Deligne-Lusztig variety has its mod l cohomology concentrated in one degree. We reduce this question to a question about tamely ramified local systems by proving that the category of perfect complexes for the group is generated by the images of the Deligne-Lusztig functors. Then, we describe the ramification at infinity of local systems associated to characters of tori.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/68105d985d0550805835481cb93e8d8b0b1d8d86

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Brauer's Height Zero Conjecture (2022, background): “A fundamental result of Bonnafé–Rouquier [5] yields that the blocks in Ep(G, s) are Morita equivalent to so-called quasi-isolated blocks of suitable Levi subgroups.”
2-blocks with abelian defect groups (2013, unknown): “(iv) G is of type E 7 or E 8 and there exists an F -stable Levi subgroup L of G , and a 2 -block C of L F such that B and C are Bonnaf´e-Rouquier correspondents, [ L , L ] F ∼ = E 6 ( q ) or 2 E 6 ( q ) and Z ◦ ( L ) F contains a defect group of C .”
Quasi-isolated blocks and Brauer’s height zero conjecture (2011, background): “Suppose that b and c are Bonnafé–Rouquier correspon- dents.”