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SUMMARY:Ziquan Yang (Harvard University)
DTSTART:20210205T230000Z
DTEND:20210206T000000Z
DTSTAMP:20260423T024730Z
UID:UCSBsga/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSBsga/10/"
 >Finiteness and the Tate Conjecture in Codimension 2 for K3 Squares</a>\nb
 y Ziquan Yang (Harvard University) as part of UCSB Seminar on Geometry and
  Arithmetic\n\n\nAbstract\nTwo years ago\, via a refined CM lifting theory
 \, Ito-Ito-Koshikawa proved the Tate Conjecture for squares of K3 surfaces
  over finite fields by reducing to Tate's theorem on the endomorphisms of 
 abelian varieties. I will explain a different proof\, which is based on a 
 twisted version of Fourier-Mukai transforms between K3 surfaces. In partic
 ular\, I do not use Tate's theorem after assuming some known properties of
  individual K3's. The main purpose of doing so is to illustrate Tate's ins
 ight on the connection between the Tate conjecture and the positivity resu
 lts in algebraic geometry for codimension 2 cycles\, through some "geometr
 y in cohomological degree 2".\n
LOCATION:https://researchseminars.org/talk/UCSBsga/10/
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