BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Marco Sangiovanni Vincentelli (Princeton University) DTSTART:20231212T210000Z DTEND:20231212T220000Z DTSTAMP:20260423T125532Z UID:MITNT/84 DESCRIPTION:Title: S elmer groups\, p-adic L-functions and Euler Systems: A Unified Framework.< /a>\nby Marco Sangiovanni Vincentelli (Princeton University) as part of MI T number theory seminar\n\nLecture held in Room 2-449 in the Simons Buildi ng (building 2).\n\nAbstract\nSelmer groups are key invariants attached to p-adic Galois representations. The Bloch—Kato conjecture predicts a pre cise relationship between the size of certain Selmer groups and the leadin g term of the L-function of the Galois representation under consideration. In particular\, when the L-function does not have a zero at s=0\, it pred icts that the Selmer group is finite and its order is controlled by the va lue of the L-function at s=0. Historically\, one of the most powerful tool s to prove such relationships is by constructing an Euler System (ES). \nA n Euler System is a collection of Galois cohomology classes over ramified abelian extensions of the base field that verify some co-restriction compa tibilities. The key feature of ESs is that they provide a way to bound Sel mer groups\, thanks to the machinery developed by Rubin\, inspired by earl ier work of Thaine\, Kolyvagin\, and Kato. In this talk\, I will present j oint work with C. Skinner\, in which we develop a new method for construct ing Euler Systems and apply it to build an ES for the Galois representatio n attached to the symmetric square of an elliptic modular form. I will str ess how this method gives a unifying approach to constructing ESs\, in tha t it can be successfully applied to retrieve most classical ESs (the cyclo tomic units ES\, the elliptic units ES\, Kato’s ES…).\n LOCATION:https://researchseminars.org/talk/MITNT/84/ END:VEVENT END:VCALENDAR