摘要翻译:
本文给出了通常的ideles群的一个推广,即我们在方案上为$k$-群的束构造了某些adelic复形。更一般地说,对于一个方案上的任何阿贝尔丛,都定义了这样的复形。我们重点讨论了一个具有某些自然公理的同调理论的束与前束相联系的情形,它是由$k$-理论所满足的。在这种情况下,我们证明了adelic复形为上述集合提供了一个flasque分解,而Gersten复形的自然态射是一个拟同构。与格斯滕分辨率相比,新的阿德利克分辨率的主要优点是它是逆变和乘法的。特别地,这使得Chow群中的交点与相应的$k$-上同调群中的自然积重合符号成为可能。我们还证明了Weil配对可以表示为具有一定指数的$k$-上同调群中的Massey三乘积。
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英文标题:
《Adelic resolution for homology sheaves》
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作者:
Sergey Gorchinskiy
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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: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:
A generalization of the usual ideles group is proposed, namely, we construct certain adelic complexes for sheaves of $K$-groups on schemes. More generally, such complexes are defined for any abelian sheaf on a scheme. We focus on the case when the sheaf is associated to the presheaf of a homology theory with certain natural axioms, satisfied by $K$-theory. In this case it is proven that the adelic complex provides a flasque resolution for the above sheaf and that the natural morphism to the Gersten complex is a quasiisomorphism. The main advantage of the new adelic resolution is that it is contravariant and multiplicative in contrast to the Gersten resolution. In particular, this allows to reprove that the intersection in Chow groups coincides up to sign with the natural product in the corresponding $K$-cohomology groups. Also, we show that the Weil pairing can be expressed as a Massey triple product in $K$-cohomology groups with certain indices.
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PDF链接:
https://arxiv.org/pdf/0705.2597