The relative Brauer group and generalized cross products for a cyclic covering of affine space

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• 作者：Timothy J. Ford ; Drake M. Harmon
• 关键词：Primary ; 16K50 ; Secondary ; 14F22 ; 14C22
• 刊名：Journal of Pure and Applied Algebra
• 出版年：April, 2014
• 年：2014
• 卷：218
• 期：4
• 页码：721-730
• 全文大小：414 K

文摘

We study algebras and divisors on a normal affine hypersurface defined by an equation of the form . The coordinate ring is , and if and , then is a cyclic Galois extension of . We show that if the Galois group is , the natural map factors through the relative Brauer group and that all of the maps are onto. Sufficient conditions are given for to be isomorphic to . As an example, all of the groups, maps, divisors and algebras are computed for an affine surface defined by an equation of the form .