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SUMMARY:SAG: A simple intrinsic proof of the Tate conjecture for K3's of f
 inite height
DTSTART:20250626T083000Z
DTEND:20250626T103000Z
DTSTAMP:20260317T062700Z
UID:indico-event-508@math-events.uni-bonn.de
DESCRIPTION:Speakers: Ziquan Yang (Hong Kong)\n\nIn the past decade\, a ma
 jor triumph for the Tate conjecture (over finite fields) is its resolution
  for K3 surfaces. However\, all known proofs rely crucially on the Kuga-Sa
 take construction—effectively outsourcing certain difficulties to the th
 eory of abelian varieties. There is an alternative approach which seeks to
  prove the conjecture by linking it to finiteness statements in arithmetic
  geometry\, and using only the geometry of K3 surfaces. The spirit of this
  approach originated in Artin and Swinnerton-Dyer’s proof for elliptic K
 3's and has recently been revitalized by Lieblich-Maulik-Snowden and Charl
 es through the moduli theory of (twisted) sheaves. In particular\, Charles
  gave an intrinsic proof assuming the Picard number is at least 2. In this
  talk\, I will explain an intrinsic proof that finite height K3's a priori
  have an even geometric Picard number\, and hence proves one step further 
 in the second approach. \n\nhttps://math-events.uni-bonn.de/event/508/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/508/
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