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Euler System Seminar, Winter 2013

Organiser: Henri Darmon
Room: Burnside Hall Lounge.

Regular Participants:
Miljan Brakocevic
Francesc Castella
Yara Elias
Clément Gomez
Bruno Joyal
Antonio Lei
Juan Ignacio Restrepo
Nicolas Simard

This seminar is aimed mainly at my graduate students and the post-docs who are working closest to me in the number theory group. The ongoing theme is the theory of Euler systems, as originally introduced by Thaine, Kolyvagin and Rubin but following its later developments building on the vision of Kato and Perrin-Riou.

A road map for the guiding theme of the seminar can be found in the survey "p-adic L-functions and Euler Systems: a tale in two trilogies". Last semester, Massimo Bertolini covered (with extra details) the material described in Sections 1.1. and 1.2. of that survey, corresponding to the Euler systems of circular and elliptic units. We will start where Bertolini left off, emphasising the material of the second part of the survey, devoted to what are referred to there as Euler systems of "Garrett-Rankin-Selberg type".

The following is a rough, tentative outline:

Thursday, January 24. Juan Restrepo. The Euler system of Heegner points, as it is presented in section 1.3 of the ``tale in two trilogies".

No date yet specified. Francesc Castella. An introduction to Kato's Euler system, fleshing out the exposition that is given in section 2.1. of the ``tale in two trilogies", and describing a proof of the p-adic Beilinson formula.

No date yet specified. Henri Darmon. Description of ongoing work with Bertolini in which Kato's reciprocity law is deduced from the material presented by Francesc.

No date yet specified. Miljan Brakocevic. Introduction to Beilinson-Flach elements, and to Hida's p-adic Rankin L-function. Proof of the p-adic Beilinson formula.

No date yet specified. Antonio Lei. The Euler system of Beilinson-Flach elements, following his article with David Loeffler and Sarah Zerbes which is now posted on the arXiv.