Number theory seminar

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24 August 2026
11:15-12:15

Dr. Eric Ahlqvist
University of Stockholm

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Title	Schur $\sigma$-groups of type $(3,3)$
Speaker, Affiliation	Dr. Eric Ahlqvist, University of Stockholm
Date, Time	24 August 2026, 11:15-12:15
Location	HG G 43
Abstract	Fix an odd prime $p$. For any imaginary quadratic field $K$, the Galois group $G_K$ of its maximal unramified pro-$p$-extension is a Schur $\sigma$-group. If the minimal number of generators of $G_K$ is at least two, then work of Golod–Shafarevich and many others implies that $G_K$ is infinite unless it has Zassenhaus type $(3,3)$, $(3,5)$, or $(3,7)$. In these three remaining cases, there is no characterization of the pairs $(K,p)$ for which $G_K$ is finite. In most cases when the Zassenhaus type is $(3,3)$, we already know that $G_K$ is $p$-adic analytic and should therefore be finite according to the Fontaine-Mazur conjecture. Regardless of that, it is an interesting problem to classify all Schur $\sigma$-groups of type $(3,3)$. In this talk, I will present recent and ongoing joint work with Richard Pink towards such a classification.

Schur $\sigma$-groups of type $(3,3)$read_more

9 October 2026
14:15-15:15

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Title TBA: Johannes Sprang

30 October 2026

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Arithmetica Transalpina

4 December 2026

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Swiss Number Theory Days

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