BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Guido Kings (Universität Regensburg)
DTSTART:20210510T170000Z
DTEND:20210510T175000Z
DTSTAMP:20260423T022920Z
UID:UCLA_NTS/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCLA_NTS/30/
 ">Equivariant Eisenstein classes\, critical values of Hecke $L$-functions 
 and $p$-adic interpolation</a>\nby Guido Kings (Universität Regensburg) a
 s part of UCLA Number Theory Seminar\n\n\nAbstract\nI report on joint work
  with Johannes Sprang. Let $K$ be a CM field and\n$L/K$ be an extension of
  degree $n$ and $\\chi$ be an algebraic critical Hecke\ncharacter of $L$. 
 Then we show that the $L$-value $L(\\chi\, 0)$ divided by\ncarefully norma
 lized Shimura-Katz periods is integral and construct a\n$p$-adic $L$-funct
 ion for $\\chi$. This generalizes results by Damerell\, Shimura and Katz f
 or CM fields ($L = K$) and settles all open cases of algebraicity for crit
 ical Hecke $L$-values.\n\nOur method relies on a detailed analysis of new 
 equivariant motivic Eisenstein classes and especially on the study of thei
 r de Rham realizations and is completely different from the classical appr
 oach by Shimura and Katz. The de Rham realization of these Eisenstein clas
 ses\ncan be explicitly described in terms of Eisenstein-Kronecker series a
 nd the equivariant setting is crucial to connect them with the $L$-functio
 n of $\\chi$. An integral refinement of this construction leads directly t
 o a geometric construction of a $p$-adic measure without any need to check
  congruences for the Eisenstein series.\n
LOCATION:https://researchseminars.org/talk/UCLA_NTS/30/
END:VEVENT
END:VCALENDAR