Euler systems and explicit reciprocity laws

Mardi 3 mars 2015 16:00-17:00 - David Loeffler - University of Warwick

Résumé : Euler systems are compatible families of classes in the cohomology of global Galois representations, which play a key role in many aspects of number theory, in particular in work on the Birch—Swinnerton-Dyer conjecture and the Iwasawa main conjecture.
Perrin-Riou has formulated a general conjecture predicting the existence of Euler systems for all Galois representations arising in geometry, but only a small handful of these are known to exist.
I will describe a construction, due to Lei, Zerbes and myself, of a new Euler system associated to the Rankin—Selberg convolution of two modular forms ; and a more recent work with Kings and Zerbes where we prove an explicit reciprocity law linking this Euler system to the critical values of L-functions. If there is time, I will also report on a current work in progress where the Rankin L-function is replaced by the Asai L-function of a quadratic Hilbert modular form.

Lieu : bât. 425 - 113-115

Euler systems and explicit reciprocity laws  Version PDF