Convolution Structures and Arithmetic Cohomology
Convolution Structures and Arithmetic Cohomology
复制标题
卷积结构和算术上同调
DOI：
10.1023/a:1023297625434
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发表时间：
1998
影响因子：
1.8
通讯作者：
A. Borisov
中科院分区：
文献类型：
--
作者：
A. Borisov
卷积结构是谐波分析师广泛研究的类群对象。我们用它们来定义数域上Arakelov因子的H 0和H1。我们证明了类似的Riemann-Roch和Serre对偶定理。这给泰特和货车德格尔和斯科夫的作品带来了更多的结构。H1的定义过程非常类似于通常的Schuerich上同调。Serre对偶成为卷积结构的Pontryagin对偶。整个理论与几何情形是平行的。
Convolution structures are group-like objects that were extensively studied by harmonic analysts. We use them to define H0 and H1 for Arakelov divisors over number fields. We prove the analogs of the Riemann–Roch and Serre duality theorems. This brings more structure to the works of Tate and van der Geer and Schoof. The H1 is defined by a procedure very similar to the usual Ĉech cohomology. Serre′s duality becomes Pontryagin duality of convolution structures. The whole theory is parallel to the geometric case.