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 ...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 integral solvability of the diophantine equation p = x2+ ny2 over a class of imaginary quadratic fields where p is a prime element.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11471314)the National Basic Research Program of China(973 Project)(Grant No.2011CB302401)the National Center for Mathematics and Interdisciplinary Sciences,Chinese Academy of Sciences
文摘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 integral solvability of the diophantine equation p = x2+ ny2 over a class of imaginary quadratic fields where p is a prime element.
