Reciprocity Laws on Algebraic Surfaces via Iterated Integrals
Abstract
This paper presents a proof of reciprocity laws for the Parshin symbol and for two new local symbols, defined here, which we call 4-function local symbols. The reciprocity laws for the Parshin symbol are proven using a new method - via iterated integrals. The usefulness of this method is shown by two facts - first, by establishing new local symbols - the 4-function local symbols and their reciprocity laws and, second, by providing refinements of the Parshin symbol in terms of bi-local symbols, each of which satisfies a reciprocity law. The K-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 the K-theoretic variant of the 4-function local symbol satisfy reciprocity laws.
Cite
@article{arxiv.1206.5817,
title = {Reciprocity Laws on Algebraic Surfaces via Iterated Integrals},
author = {Ivan Horozov and Matt Kerr},
journal= {arXiv preprint arXiv:1206.5817},
year = {2018}
}
Comments
A second 4-fucntion local symbol is introduced. The approach via iterated integrals is structured better. We use more Milnor K-groups. 30 pages