The cohomology of Deligne-Lusztig varieties for the general linear group

被引：1
|
作者：
Orlik, Sascha [1 ]
机构：
[1] Berg Univ Wuppertal, Fachbereich Math & Nat Wissensch C, Gaussstr 20, D-42119 Wuppertal, Germany
来源：
RESEARCH IN THE MATHEMATICAL SCIENCES | 2018年 / 5卷
关键词：
REGULAR ELEMENTS; REDUCTIVE GROUPS; FINITE; REPRESENTATIONS; CHARACTERS;
D O I：
10.1007/s40687-018-0131-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We propose two inductive approaches for determining the cohomology of Deligne-Lusztig varieties in the case of G = GL(n). The first one uses Demazure compactifications and analyzes the corresponding Mayer-Vietoris spectral sequence. This allows us to give an inductive formula for the Tate twist -1 contribution of the cohomology of a DL-variety. The second approach relies on considering more generally DL-varieties attached to hypersquares in the Weyl group. Here we give explicit formulas for the cohomology of height-one elements.
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页数：71
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