A General Reciprocity Law for Symbols on Arbitrary Vector Spaces
Number Theory
2020-07-07 v1 Algebraic Geometry
Abstract
The aim of this work is to offer a general theory of reciprocity laws for symbols on arbitrary vector spaces, and to show that classical explicit reciprocity laws are particular cases of this theory (sum of valuations on a complete curve, Residue Theorem, Weil Reciprocity Law and the Reciprocity Law for the Hilbert Norm Residue Symbol). Moreover, several reciprocity laws introduced over the past few years by D. V. Osipov, A. N. Parshin, I. Horozov, I. Horozov - M. Kerr and the author -together with D. Hern\'andez Serrano-, can also be deduced from this general expression.
Keywords
Cite
@article{arxiv.1305.7066,
title = {A General Reciprocity Law for Symbols on Arbitrary Vector Spaces},
author = {Fernando Pablos Romo},
journal= {arXiv preprint arXiv:1305.7066},
year = {2020}
}