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Euler-Kolyvagin system machinery is used to compute the size of a Selmer group in terms of the special values of the relevant L-function. Kato has constructed an Euler system attached to modular forms using Beilinson elements using which he was able to deduce striking results towards the conjecture of Birch and Swinnerton-Dyer. The principal goal of this talk is to prove that the Kolyvagin systems associated to Beilinson-Kato elements interpolate in the full deformation space, generalizing Ochiai‘s prior work where he was able to prove a similar statement on the ordinary locus. we exhibit applications of our *big* Kolyvagin system towards Greenberg’s main conjectures, by defining (among other things) an ideal of the analytic generic fiber of the universal deformation space, that behaves like an algebraic p-adic L-function (in 3-variables).
Donnerstag, den 8. Mai 2014 um 17.15 Uhr Uhr, in INF 288, HS2 Donnerstag, den 8. Mai 2014 at 17.15 Uhr, in INF 288, HS2
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. G. Böckle