Number Theory Seminar
- Event Type
- Seminar/Symposium
- Sponsor
- Department of Mathematics
- Location
- Altgeld Hall 141
- Date
- Mar 25, 2025 11:00 - 11:50 am
- Speaker
- Alexander Smith (UCLA)
- Contact
- Jesse Thorner and Yuan Liu
- jat9@illinois.edu and yyyliu@illinois.edu
- Views
- 76
- Originating Calendar
- Number Theory Seminar Calendar
Title: Faithful characters and the Chebotarev density theorem (jt. with Robert Lemke-Oliver)
Abstract: Choose a finite group G and a number field F. We show that, given any large family of G-extensions of F, almost all are subject to a strong effective form of the Chebotarev density theorem. As one consequence, given a prime p, we are able to give nontrivial upper bounds for the size of the p-torsion of the class group of most G-extensions of F.
To prove this result requires a tool we have developed in the character theory of finite groups. More specifically, it requires a strengthened form of Artin's induction theorem that applies to faithful irreducible characters.