10월2일 금 10:30-12:00 27동325호
세미나 종류 정수론/dasom
연사 Oussama Rayen Hamza
소속 Harbin Institute of Technology

Title: Filtrations and Graph Theory: Applications in Galois Theory and Arithmetic

Abstract: Graph products, filtrations, and cohomology rings provide useful tools for studying pro-p Galois groups.

I will first present joint work with Maire, Mináč, and Tân on formally real Pythagorean fields of finite type (RPF fields). In this work, a new class of groups, called Delta-Right Angled Artin groups, is introduced. This class provides a new necessary condition for maximal pro-2 Galois groups. As an application, this work constructs a pro-2 group that is not a maximal pro-2 Galois group, although it satisfies the Koszul, strong Massey vanishing, and Kernel Unipotent properties.

I will then discuss pro-p extensions of number fields, when p is an odd prime, with restricted ramification and prescribed splitting. In the wild case (ramification containing places above p), joint work with Lim and Maire uses coproduct decompositions and Massey vanishing to construct large unipotent extensions. In the tame case (ramification not containing places above p), analogously to knot theory, we have a notion of linking numbers for some of these extensions. In joint work with Feuerpfeil and Lim, we answer a question of Labute on the realization of linking numbers and derive several cohomological consequences.