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SUMMARY:Chao Li (Columbia Univ.)
DTSTART:20210126T210000Z
DTEND:20210126T220000Z
DTSTAMP:20260423T041623Z
UID:UAANTS/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UAANTS/13/">
 Beilinson-Bloch conjecture for unitary Shimura varieties</a>\nby Chao Li (
 Columbia Univ.) as part of University of Arizona Algebra and Number Theory
  Seminar\n\n\nAbstract\nFor certain automorphic representations $\\pi$ on 
 unitary groups\, we show that if $L(s\, \\pi)$ vanishes to order one at th
 e center $s=1/2$\, then the associated $\\pi$-localized Chow group of a un
 itary Shimura variety is nontrivial. This proves part of the Beilinson-Blo
 ch conjecture for unitary Shimura varieties\, which generalizes the BSD co
 njecture. Assuming the modularity of Kudla's generating series of special 
 cycles\, we further prove a precise height formula for $L'(1/2\, \\pi)$. T
 his proves the conjectural arithmetic inner product formula\, which genera
 lizes the Gross-Zagier formula to Shimura varieties of higher dimension. W
 e will motivate these conjectures and discuss some aspects of the proof. T
 his is joint work with Yifeng Liu.\n
LOCATION:https://researchseminars.org/talk/UAANTS/13/
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