Abstract
AbstractIn this paper we introduce new local symbols, which we call 4-function local symbols. We formulate reciprocity laws for them. These reciprocity laws are proven using a new method - multidimensional iterated integrals. Besides providing reciprocity laws for the new 4-function local symbols, the same method works for proving reciprocity laws for the Parshin symbol. Both the new 4-function local symbols and the Parshin symbol can be expressed as a finite product of newly defined bi-local symbols, each of which satisfies a reciprocity law. TheK-theoretic variant of the first 4-function local symbol is defined in the Appendix. It differs by a sign from the one defined via iterated integrals. Both the sign and theK-theoretic variant of the 4-function local symbol satisfy reciprocity laws, whose proof is based on MilnorK-theory (see the Appendix). The relation of the 4-function local symbols to the double free loop space of the surface is given by iterated integrals over membranes.
Publisher
Cambridge University Press (CUP)
Subject
Geometry and Topology,Algebra and Number Theory
Reference31 articles.
1. Sur les fonctions algébriques á corps de constantes fini;Weil;C. R. Acad. Sci. Paris,1940
2. Nodes and the Hodge conjecture
3. Chow groups with coefficients;Rost;Doc. Math.,1996
4. Algebraic construction of the tame symbol and the Parshin symbol on a surface
5. Local class field theory;Parshin;Trudy Mat. Inst. Steklov,1984
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