Non-splitting of the Hilbert exact sequence via a principal version of the Chebotarev density theorem

Abstract: Let $K/k$ be a Galois extension of number fields and $C$ a conjugacy class of $\text{Gal}(K/k)$. In this talk, we will investigate the density of prime ideals of $k$ which factor as the product of principal ideals in $K$ and have their associated Frobenius class equal to $C$. From this density we will determine a method for verifying the nonsplitting of the Hilbert exact sequence.

number theory

Audience: researchers in the discipline

Comments: Register here: umanitoba.zoom.us/meeting/register/u5csf-CtqzstEtfTaoLl6L8gnaVIJnGVB49w

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POINT: New Developments in Number Theory

Series comments: There will be two 20-minute contributed talks during each meeting aimed at a general number theory audience, including graduate students.

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