“Bloch-Kato pro-$p$ groups and toric arrangements”
Venerdì 20 Giugno 2025, ore 14:30 - Aula 2AB45 - Ettore Marmo (Università degli Studi di Milano-Bicocca)
Abstract
For every field $K$ we can define a distinguished extension $K^{\mathrm{sep}}$ called its separable closure. The maximal pro-$p$ quotient $G_K(p)$ of the Galois group $G_K = \mathrm{Gal}(K^{\mathrm{sep}}/K)$ is called the maximal pro-$p$ Galois group of $K$, many arithmetical properties of the field are encoded in the structure of this group. It is interesting to ask which pro-$p$ groups can be realized as the maximal pro-$p$ Galois group of some field. It is known that any such group must also satisfy a cohomological property called the Bloch-Kato property. In this talk we will discuss some families of pro-$p$ groups arising as from toric arrangements and some techniques to study the Bloch-Kato property in this context.
This talk is based on joint work with Th. Weigel and E. Delucchi.
