摘要翻译:
设G是作用于方案X的连通约化代数群,设R(G)表示G的表示环,设I是秩为0的虚表示的R(G)中的理想。设G(X)(即G(G,X))表示X上相干束(即G-等变相干束)的Grothendieck群。Merkurjev证明了如果G的基本群是无扭的,则G(G,X)/IG(G,X)到G(X)的映射是同构的。虽然当G的基本群具有扭转时,这个映射不一定是同构的,但我们证明了在没有关于G的基本群的假设的情况下,这个映射与有理数张量后是同构的。
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英文标题:
《The forgetful map in rational K-theory》
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作者:
William Graham
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最新提交年份:
2007
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分类信息:
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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一级分类:Mathematics 数学
二级分类:K-Theory and Homology K-理论与同调
分类描述:Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
代数和拓扑K-理论,与拓扑的关系,交换代数和算子代数
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英文摘要:
Let G be a connected reductive algebraic group acting on a scheme X. Let R(G) denote the representation ring of G, and let I be the ideal in R(G) of virtual representations of rank 0. Let G(X) (resp. G(G,X)) denote the Grothendieck group of coherent sheaves (resp. G-equivariant coherent sheaves) on X. Merkurjev proved that if the fundamental group of G is torsion-free, then the map of G(G,X)/IG(G,X) to G(X) is an isomorphism. Although this map need not be an isomorphism if the fundamental group of G has torsion, we prove that without the assumption on the fundamental group of G, this map is an isomorphism after tensoring with the rational numbers.
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PDF链接:
https://arxiv.org/pdf/0710.1253