Monthly Archives: July 2009

Dedekind Domains in Finite Galois Extensions

Posted on July 14, 2009 by Jim Stankewicz

Last time we examined Dedekind domains in finite separable field extensions. One advantage to using a separable field extension that we did not use is that we can base extend to a finite Galois extension, where as we see the … Continue reading →

Posted in Algebraic Number Theory, Curves, Number Fields, Uncategorized | Leave a comment

Dedekind Domains in finite separable extensions

Posted on July 8, 2009 by Jim Stankewicz

Last time we took a look at Dedekind domains with fraction fields and found that if was any finite field extension of that the integral closure of in is Dedekind. The proof in this case is somewhat involved, but becomes … Continue reading →

Posted in Uncategorized | 5 Comments

Dedekind Domains, Krull-Akizuki and the Picard Group

Posted on July 2, 2009 by Jim Stankewicz

As has been hinted in many previous posts, many facts about algebraic number theory tell us about geometric objects like elliptic curves. For instance, if you are working on a problem which primarily uses the affine geometry of a curve … Continue reading →

Posted in Curves, Uncategorized | 5 Comments