K-cohomology of Severi-Brauer Varieties and the norm residue homomorphism
K-cohomology of Severi-Brauer Varieties and the norm residue homomorphism
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DOI：
10.1070/im1983v021n02abeh001793
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发表时间：
1983-04
期刊：
影响因子：
--
通讯作者：
A. S. Merkur’ev;A. Suslin
中科院分区：
文献类型：
--
作者：
A. S. Merkur’ev;A. Suslin
本文的基本目的是证明特征素为的域的模剩余同态的双射性。特别地，如果，则任何指数的中心单代数类似于循环代数的张量积。在证明过程中，我们得到了Gersten谱序列的部分退化性，并计算了与素度循环代数相对应的Severi-Brauer群的-上同调群。基本定理也给我们几个推论。书目：27种。
The basic purpose of this paper is to prove bijectivity of the norm residue homomorphism for any field of characteristic prime to . In particular, if , then any central simple algebra of exponent is similar to a tensor product of cyclic algebras. In the course of the proof we obtain partial degeneracy of the Gersten spectral sequence, and we compute some -cohomology groups of Severi-Brauer groups corresponding to cyclic algebras of prime degree. The fundamental theorem also gives us several corollaries. Bibliography: 27 titles.