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SUMMARY:Shou-Wu Zhang (Princeton University)
DTSTART:20200922T203000Z
DTEND:20200922T213000Z
DTSTAMP:20260423T125532Z
UID:MITNT/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/8/">De
 composition theorems for arithmetic cycles</a>\nby Shou-Wu Zhang (Princeto
 n University) as part of MIT number theory seminar\n\n\nAbstract\nWe will 
 describe    some decomposition theorems for  cycles over polarized  variet
 ies in both local and global settings   under   some conjectures of Lefsch
 etz type.  In local settings\, our  decomposition theorems are essentially
   non-archimedean analogues of  ``harmonic forms" on Kahler manifolds. As 
 an application\, we will define   a notion of   ``admissible pairings" of 
 algebraic cycles  which is a simultaneous  generalization of Beilinson--Bl
 och height pairing\, and the  local  intersection pairings \ndeveloped by 
 Arakelov\,  Faltings\,   and  Gillet--Soule  on Kahler manifolds.  In glob
 al setting\,\nour decomposition theorems provide  canonical  splittings of
  some canonical filtrations\, including  canonical liftings of homological
  cycles to algebraic cycles.\n
LOCATION:https://researchseminars.org/talk/MITNT/8/
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