Oct 12, 2023
Weak approximation on the norm one torus
Algebraic Geometry and Number Theory Seminar
Date: October 12, 2023 |
1:00 pm –
3:00 pm
Speaker:
Peter Koymans, ETH Zürich
Location: Heinzel Seminar Room (I21.EG.101), Office Building West, ISTA
Language:
English
For any abelian group A, we prove an asymptotic formula for the number of A-extensions K/Q of bounded discriminant such that the associated norm one torus R_{K/Q}^1 G_m satisfies weak approximation. We will discuss how to parametrise abelian extensions in a convenient way so that the problem reduces to the estimation of a certain character sum. We will then estimate this character sum using Siegel–Walfisz and the large sieve. This is joint work with Nick Rome.
