Gautier Ponsinet (Université Bordeaux)

The Bloch-Kato Selmer groups associated with a geometric representation of the Galois group of a number field take part in Bloch and Kato's conjecture on the special values of L functions of motives. In Iwasawa theory, we are interested in the structure of these Bloch-Kato Selmer groups over infinite algebraic fields extensions. To do so, we need to study the local Bloch-Kato groups defined via p-adic Hodge theory. In this talk, I will present new results about the local Bloch-Kato groups over perfectoid fields, thereby answering a question by Coates and Greenberg in new cases. These local results allow to describe the Bloch-Kato Selmer groups over many infinite extensions as Selmer groups "à la Greenberg" which are easier to handle. If time allows, I will present immediate consequences of this description in Iwasawa theory.

livestream:
http://129.206.106.240/UzPL29kB/mathematikon-seminarraum.html