On Orders in Number Fields: Picard Groups, Ring Class Fields and Applications
Number Theory
2016-12-06 v3
Abstract
In this article, we focus on orders in arbitrary number fields, consider their Picard groups and finally obtain ring class fields corresponding to them. The Galois group of the ring class field is isomorphic to the Picard group. As an application, we give criteria of the solvability of the diophantine equation over a class of imaginary quadratic fields where is a prime element.
Cite
@article{arxiv.1405.5776,
title = {On Orders in Number Fields: Picard Groups, Ring Class Fields and Applications},
author = {Chang Lv and Yingpu Deng},
journal= {arXiv preprint arXiv:1405.5776},
year = {2016}
}
Comments
13 pages, this version (date: Aug 8, 2014; git commit:20140627a/db806a6) has been accepted for publication in SCIENCE CHINA Mathematics on Jan 4, 2015. arXiv admin note: substantial text overlap with arXiv:1405.7109