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- W1519861480 abstract "We study the cohomology of parabolic Deligne-Lusztig varieties associated to unipotent blocks of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper G normal upper L Subscript n Baseline left-parenthesis q right-parenthesis> <mml:semantics> <mml:mrow> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>G</mml:mi> <mml:mi mathvariant=normal>L</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>q</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>mathrm {GL}_n(q)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We show that the geometric version of Broué’s conjecture over <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper Q overbar Subscript script l> <mml:semantics> <mml:msub> <mml:mover> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>Q</mml:mi> </mml:mrow> <mml:mo accent=false>¯<!-- ¯ --></mml:mo> </mml:mover> <mml:mi>ℓ<!-- ℓ --></mml:mi> </mml:msub> <mml:annotation encoding=application/x-tex>overline {mathbb {Q}}_ell</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, together with Craven’s formula, holds for any unipotent block whenever it holds for the principal <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Phi 1> <mml:semantics> <mml:msub> <mml:mi mathvariant=normal>Φ<!-- Φ --></mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:annotation encoding=application/x-tex>Phi _1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-block." @default.
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- W1519861480 date "2013-12-10" @default.
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- W1519861480 title "Cohomology of Deligne-Lusztig varieties for unipotent blocks of 𝐺𝐿_{𝑛}(𝑞)" @default.
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- W1519861480 doi "https://doi.org/10.1090/s1088-4165-2013-00446-6" @default.
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