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• W2009761289 abstract "Let X be a scheme of finite type over a Noetherian base scheme S admitting a dualizing complex, and let U be an open subset whose complement has codimension at least 2. We extend the Deligne-Bezrukavnikov theory of perverse coherent sheaves by showing that a coherent middle extension (or intersection cohomology) functor from perverse sheaves on U to perverse sheaves on X may be defined for a much broader class of perversities than has previously been known. We also introduce a derived category version of the coherent middle extension functor. Under suitable hypotheses, we introduce a construction (called S2-extension) in terms of perverse coherent sheaves of algebras on X that takes a finite morphism to U and extends it in a canonical way to a finite morphism to X. In particular, this construction gives a canonical S2-ification of appropriate X. The construction also has applications to the Macaulayfication problem, and it is particularly well-behaved when X is Gorenstein. Our main goal, however, is to address a conjecture of Lusztig on the geometry of special pieces (certain subvarieties of the unipotent variety of a reductive algebraic group). The conjecture asserts in part that each special piece is the quotient of some variety (previously unknown in the exceptional groups and in positive characteristic) by the action of a certain finite group. We use S2-extension to give a uniform construction of the desired variety." @default.
• W2009761289 created "2016-06-24" @default.
• W2009761289 creator A5024026387 @default.
• W2009761289 creator A5083785442 @default.
• W2009761289 date "2009-03-01" @default.
• W2009761289 modified "2023-09-25" @default.
• W2009761289 title "Perverse coherent sheaves and the geometry of special pieces in the unipotent variety" @default.
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• W2009761289 doi "https://doi.org/10.1016/j.aim.2008.10.012" @default.
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