Complexes de chaı̂nes étales et courbes de Deligne–Lusztig

✍ Scribed by Raphaël Rouquier

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 230 KB
• Volume: 257
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(02)00530-6

✦ Synopsis

In a first part, we lift the usual constructions of functors between derived categories of étale sheaves over schemes with a sheaf of algebras to pure derived categories. For varieties with finite group actions, we recover, in a more functorial way, Rickard's construction.

We apply this to the case of Deligne-Lusztig varieties and show that Broué's conjecture holds for curves. The additional ingredient we need is obtained from an easy property of the cohomology of etale covers of the affine line.