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SUMMARY:The weakly special conjecture contradicts Orbifold Mordell\, and h
 ence abc - Special session of the HyperK seminar in Bonn on January 9 & 10
 \, 2025
DTSTART:20250110T080000Z
DTEND:20250110T090000Z
DTSTAMP:20260420T152800Z
UID:indico-event-177@math-events.uni-bonn.de
CONTACT:huybrech@math.uni-bonn.de
DESCRIPTION:Speakers: Ariyan Javanpeykar (Nijmegen)\n\nAbstract: Lang conj
 ectured that varieties of general type over a number field have very few r
 ational points. In 2000\, guided by Lang's conjecture and in search of a c
 onverse statement\, Abramovich\, Colliot-Thelene\, Harris\, and Tschinkel 
 formulated the "Weakly Special Conjecture": every weakly special variety o
 ver a number field has a potentially dense set of rational points. In this
  talk I will explain how this conjecture contradicts the abc conjecture\, 
 and more precisely Campana's "Orbifold Mordell" conjecture. Indeed\, start
 ing from an Enriques surface over Q(t) constructed by Lafon\, we give the 
 first examples of smooth projective weakly special threefolds which fiber 
 over the projective line in Enriques surfaces with nowhere reduced\, but n
 on-divisible\, fibers. The existence of these threefolds shows that the We
 akly Special Conjecture contradicts the abc conjecture\, but also shows th
 at Enriques surfaces and K3 surfaces can have non-divisible but nowhere re
 duced degenerations\, thereby answering a question raised by Campana in 20
 05. This is joint work with Finn Bartsch\, Frederic Campana\, and Olivier 
 Wittenberg.\n\nhttps://math-events.uni-bonn.de/event/177/
LOCATION:Poppelsdorfer Allee 45\, 1\, EG\, Lecture room - HIM PA82 (HIM)
URL:https://math-events.uni-bonn.de/event/177/
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