Ruprecht-Karls-Universität Heidelberg
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„Bloch-Kato groups, perfectoid fields, and Iwasawa theory“
Dr. Gautier Ponsinet, Université de 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.

Freitag, den 2. Dezember 2022 um 13:30 Uhr, in INF 205, SR A Freitag, den 2. Dezember 2022 at 13:30, in INF 205, SR A

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Dr. Otmar Venjakob