Logarithmic Functional and the Weil Reciprocity Law
نویسنده
چکیده
This article is devoted to the (one-dimensional) logarithmic functional with argument being one-dimensional cycle in the group (C∗)2. This functional generalizes usual logarithm, that can be viewed as zero-dimensional logarithmic functional. Logarithmic functional inherits multiplicative property of the logarithm. It generalizes the functional introduced by Beilinson for topological proof of the Weil reciprocity law. Beilinson’s proof is discussed in details in this article. Logarithmic functional can be easily generalized for multidimensional case. It’s multidimensional analog (see Ref. 5) proves multidimensional reciprocity laws of Parshin. I plan to return to this topic in upcoming publications.
منابع مشابه
Logarithmic functional and reciprocity laws
In this paper, we give a short survey of results related to the reciprocity laws over the field C. We announce a visual topological proof of Parshin’s multidimensional reciprocity laws over C. We introduce the logarithmic functional, whose argument is an n-dimensional cycle in the group (C∗)n+1. It generalizes the usual logarithm, which can be considered as the zero-dimensional logarithmic func...
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