反向相干槽与特殊片的几何形状 单性变种

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摘要翻译：
设X是Noetherian基格式S上的有限型格式，允许对偶复形；设U是补余维数至少为2的开子集。我们推广了反常相干束的Deligne-Bezrukavnikov理论，证明了从U上的反常束到X上的反常束的相干中延（或交上同调）函子可以定义为比以前已知的更广泛的反常类。我们还引入了相干中间扩张函子的一个派生范畴版本。在适当的假设下，我们引入了一个关于X上代数的逆相干束的构造（称为“S2-扩张”），它将有限态射推广到U,并以规范的方式将其推广到X的有限态射。特别地，这个构造给出了适当X的规范的“S2-化”。该构造也应用于“Macaulaydation”问题，尤其是当X是Gorenstein时，它表现得很好。然而，我们的主要目标是解决Lusztig关于特殊片（约化代数群的一个幂次变体的某些子变体）几何的一个猜想。该猜想部分地断言，每一特殊块都是某种变体（以前在例外群和正特征中未知）在某个有限群的作用下的商。我们用S2-扩张给出了所需变体的统一构造。
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英文标题：
《Perverse coherent sheaves and the geometry of special pieces in the
  unipotent variety》
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作者：
Pramod N. Achar, Daniel S. Sage
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Representation Theory        表象理论
分类描述：Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra
代数和群的线性表示，李理论，结合代数，多重线性代数
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  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.
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PDF链接：
https://arxiv.org/pdf/0707.0088

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关键词：Construction Presentation Applications mathematics Presentatio variety 变体 给出 extension 格式