SEMINARIO TEORÍA DE GRUPOS

Oriented pro-p RAAGs and Galois cohomology

Ponente: Simone Blumer (University of Milano-Bicocca/University of Zaragoza)

Fecha: Lunes, 24 de octubre de 2022 - 11:00

Lugar: Aula Naranja, ICMAT

Resumen:

One of the main open problems in recent Galois theory concerns the recognition of those profinite groups that occur as absolute Galois groups. Many attempts of detecting realizability of profinite groups as absolute Galois groups rely on cohomological aspects and many conjectures have been suggested. In particular, since a proof of the Bloch-Kato conjecture was provided in 2011, quadraticity of the group cohomology ring has become one of great interest. In a joint work with C. Quadrelli and Th. Weigel, we considered a certain class of groups generalizing the pro-p completion of classical RAAGs; our study corroborates the main conjectures in this context, and, on the other hand, it provides a huge class of pro-p groups that do not occur as absolute Galois groups. In fact, the class of the discrete right-angled Artin groups plays an important role in geometric group theory, since it generalizes both the classes of the free groups and of the free-abelian groups, and it provides a large test bed for those conjectures.