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Weak approximation on the norm one torus

Algebraic Geometry and Number Theory Seminar

Date: Thursday, October 12, 2023 13:00 - 15:00
Speaker: Peter Koymans (ETH Z├╝rich)
Location: Heinzel Seminar Room (I21.EG.101), Office Building West, ISTA
Series: Mathematics and CS Seminar
Host: Tim Browning

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.

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