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SUMMARY:Chao Li (Columbia University)
DTSTART:20210217T160000Z
DTEND:20210217T170000Z
DTSTAMP:20260418T064042Z
UID:LNTS/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/29/">Be
 ilinson-Bloch conjecture for unitary Shimura varieties</a>\nby Chao Li (Co
 lumbia University) as part of London number theory seminar\n\n\nAbstract\n
 For certain automorphic representations $\\pi$ on unitary groups\, we show
  that if $L(s\, \\pi)$ vanishes to order one at the center $s=1/2$\, then 
 the associated $\\pi$-localized Chow group of a unitary Shimura variety is
  nontrivial. This proves part of the Beilinson-Bloch conjecture for unitar
 y Shimura varieties\, which generalizes the BSD conjecture. Assuming Kudla
 's modularity conjecture\, we further prove the arithmetic inner product f
 ormula for $L'(1/2\, \\pi)$\, which generalizes the Gross-Zagier formula. 
 We will motivate these conjectures and discuss some aspects of the proof. 
 We will also mention recent extensions applicable to certain symmetric pow
 er L-functions of elliptic curves. This is joint work with Yifeng Liu.\n
LOCATION:https://researchseminars.org/talk/LNTS/29/
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