BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Waqar Shah (UCSB) DTSTART:20220929T233000Z DTEND:20220930T010000Z DTSTAMP:20260423T023937Z UID:UCSBsga/38 DESCRIPTION:Title: Zeta elements for Shimura Varieties I: Generalities\nby Waqar Shah (U CSB) as part of UCSB Seminar on Geometry and Arithmetic\n\n\nAbstract\nA w ell-established technique towards understanding Selmer groups of Galois re presentations is the construction of an Euler system. One may ask if such systems can be created for Galois representations that arise in the cohomo logy of a given Shimura variety. For such purposes\, it is customary to ut ilize push-forwards of fundamental cycles or Eisenstein classes from sub-S himura varieties\, and to then establish norm relations between the push-f orwarded classes involving certain Hecke operators which compute appropria te automorphic L-factors.\n\nIn this talk\, I will motivate how classical Euler systems such as Kato's Siegel units and Kolyvagin's Heegner points m ay be viewed through an axiomatic lens and build up to a general framework in which norm relations for higher dimensional Shimura varieties may be s ystematically studied. I will highlight some of the computational challeng es that arise in higher dimensions and outline a theory of double coset de compositions due to Lansky that allows one to overcome these challenges. I n the next talk\, I'll apply these techniques to concrete examples of arit hmetic interest\, some old and some new.\n LOCATION:https://researchseminars.org/talk/UCSBsga/38/ END:VEVENT END:VCALENDAR