Monday 1st December 2025 at 3 pm, as part of the Al@Bicocca seminar cycle, Ettore Marmo (University of Milano-Bicocca) will give the following talk
Title: Toric arrangements and Bloch-Kato pro-p groups
Abstract: The absolute Galois group of a field K is defined as the Galois group of the distinguished extension Ksep/K given by the separable closure. A challenging problem in modern Galois theory is to recognize which pro-p groups can be realized as maximal pro-p quotients of an absolute Galois group. Such pro-p groups must satisfy a rather strong cohomological condition called Bloch-Kato property. In this talk we will discuss some obstructions to this property for a class of pro-p groups arising as the pro-p completion of fundamental groups of toric arrangement complements. As an application, we will prove that for all primes p, the pro-p completion of the pure braid groups on n ≥ 4 strands do not satisfy the Bloch-Kato property.
Information to attend
The seminar will be held in Room U6-24 (U6 Building | 1st Floor | Piazza dell'Ateneo Nuovo 1, Milano) and will also be available online by this link.
For more information, visit the website