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SUMMARY:Liang Xiao (Peking International Center for Mathematical Research)
DTSTART:20220104T070000Z
DTEND:20220104T083000Z
DTSTAMP:20260423T041505Z
UID:viasmag/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/viasmag/4/">
 Beilinson--Bloch--Kato conjecture for some Rankin-Selberg motives.</a>\nby
  Liang Xiao (Peking International Center for Mathematical Research) as par
 t of VIASM Arithmetic Geometry Online Seminar\n\nLecture held in C101\, VI
 ASM.\n\nAbstract\nThe Birch and Swinnerton-Dyer conjecture is known in the
  case of rank $0$ and $1$ thanks to the foundational work of Kolyvagin and
  Gross-Zagier. In this talk\, I will report on a joint work with Yifeng Li
 u\, Yichao Tian\, Wei Zhang\, and Xinwen Zhu. We study the analogue and ge
 neralizations of Kolyvagin's result to the unitary Gan-Gross-Prasad paradi
 gm. More precisely\, our ultimate goal is to show that\, under some techni
 cal conditions\, if the central value of the Rankin-Selberg $L$-function o
 f an automorphic representation of $U(n) \\ast U(n+1)$ is nonzero\, then t
 he associated Selmer group is trivial\; Analogously\, if the Selmer class 
 of certain cycle for the $U(n) \\ast U(n+1)$-Shimura variety is nontrivial
 \, then the dimension of the corresponding Selmer group is one. ($\\href{h
 ttps://drive.google.com/file/d/1crDh5JwaFv8HW7wZ3NZtDugaFQHOZrTG/view?usp=
 sharing}{{\\rm notes}}$).\n
LOCATION:https://researchseminars.org/talk/viasmag/4/
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