Document Type
Article
Publication Date
2002
Department 1
Mathematics
Abstract
We give a condition on a family of solutions of quotients of an embedding problem which implies the embedding problem has a solution. This shows, in particular, that to solve an embedding problem associated to the maximal extension of a number field unramified outside a fixed finite set of places, it suffices to find a solution for each finite quotient of the embedding problem. This statement is not true in general over global function fields, but one can prove variants of it in this case in which extra conditions on the embedding problems or on the ramification of solutions are assumed.
Copyright Note
This is the publisher's version of the work. This publication appears in Gettysburg College's institutional repository by permission of the copyright owner for personal use, not for redistribution.
Recommended Citation
Chinburg T, and D. Glass, Embedding Problems and Finite Quotients. Pacific Journal of Mathematics. 2002. 205(1): 31-41.