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SUMMARY:Yifeng Liu (Yale)
DTSTART:20200617T130000Z
DTEND:20200617T140000Z
DTSTAMP:20260418T064517Z
UID:LNTS/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/9/">Bei
 linson-Bloch conjecture and arithmetic inner product formula</a>\nby Yifen
 g Liu (Yale) as part of London number theory seminar\n\n\nAbstract\nIn thi
 s talk\, we study the Chow group of the motive associated to a tempered gl
 obal $L$-packet $\\pi$ of unitary groups of even rank with respect to a CM
  extension\, whose global root number is $-1$. We show that\, under some r
 estrictions on the ramification of $\\pi$\, if the central derivative $L'(
 1/2\,\\pi)$ is nonvanishing\, then the $\\pi$-nearly isotypic localization
  of the Chow group of a certain unitary Shimura variety over its reflex fi
 eld does not vanish. This proves part of the Beilinson--Bloch conjecture f
 or Chow groups and L-functions (which generalizes the B-SD conjecture). Mo
 reover\, assuming the modularity of Kudla's generating functions of specia
 l cycles\, we explicitly construct elements in a certain $\\pi$-nearly iso
 typic subspace of the Chow group by arithmetic theta lifting\, and compute
  their heights in terms of the central derivative $L'(1/2\,\\pi)$ and loca
 l doubling zeta integrals. This confirms the conjectural arithmetic inner 
 product formula proposed by me a decade ago. This is a joint work with Cha
 o Li.\n
LOCATION:https://researchseminars.org/talk/LNTS/9/
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