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SUMMARY:Yifeng Liu (Yale University)
DTSTART:20201120T000000Z
DTEND:20201120T010000Z
DTSTAMP:20260423T022806Z
UID:UCSD_NTS/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSD_NTS/16/
 ">Beilinson-Bloch conjecture and arithmetic inner product formula</a>\nby 
 Yifeng Liu (Yale University) as part of UCSD number theory seminar\n\nLect
 ure held in normally APM 7321\, currently online.\n\nAbstract\nIn this tal
 k\, we study the Chow group of the motive associated to a tempered global 
 L-packet \\pi of unitary groups of even rank with respect to a CM extensio
 n\, whose global root number is -1. We show that\, under some restrictions
  on the ramification of \\pi\, if the central derivative L'(1/2\,\\pi) is 
 nonvanishing\, then the \\pi-nearly isotypic localization of the Chow grou
 p of a certain unitary Shimura variety over its reflex field does not vani
 sh. This proves part of the Beilinson--Bloch conjecture for Chow groups an
 d L-functions. Moreover\, assuming the modularity of Kudla's generating fu
 nctions of special cycles\, we explicitly construct elements in a certain 
 \\pi-nearly isotypic subspace of the Chow group by arithmetic theta liftin
 g\, and compute their heights in terms of the central derivative L'(1/2\,\
 \pi) and local doubling zeta integrals. This is a joint work with Chao Li.
 \n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/16/
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