MATH Seminar
| Title: An algebraic approach to enumerating field extensions |
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| Seminar: Algebra |
| Speaker: Frank Thorne of University of South Carolina |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2014-09-22 at 4:00PM |
| Venue: W302 |
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| Abstract: Building on previous work of Cohen and several of his collaborators, I will discuss the use Kummer theory and class field theory to enumerate field extensions of low degree. We obtain an explicit Dirichlet series representation, in the form of a finite sum of Euler products, for the set of field extensions with Galois group $S_3, A_4, S_4$, or $D_l$ (l an odd prime) with fixed resolvent. This has a variety of interesting consquences, including results on the Shintani zeta function as well as an extension of the Scholz reflection principle, which I will describe. Most of this is joint work with Henri Cohen, and one part is also joint with Simon Rubinstein-Salzedo. |
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