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SUMMARY:Non-density of transcendental-rational points on Bogomolov-Tschink
el's weakly-special non-special threefolds
DTSTART:20240320T140000Z
DTEND:20240320T150000Z
DTSTAMP:20240530T160200Z
UID:indico-event-240@events.dm.unipi.it
DESCRIPTION:Speakers: Ariyan Javanpeykar (Nijmegen)\n\nWhat varieties shou
ld have a dense set of rational points? Campana's conjectures from the ear
ly 2000s predict that a smooth projective variety over a number field has
a potentially dense set of rational points if and only if it is special.
This conjecture is in conflict with the Weakly Special Conjecture (also fo
rmulated in the early 2000s). The latter predicts potential density hol
ds for all weakly special varieties. However\, Bogomolov-Tschinkel constru
cted the first example of a non-special weakly-special variety which shows
the conflict. Now\, Abramovich and Varilly-Alvarado showed that Vojta'
s higher-dimensional abc conjecture implies that the Weakly Special Conjec
ture is false\, so presumably Campana is right. However\, up until today\,
we do not have a single (unconditional) example of a non-special weakly-s
pecial threefold whose rational points are not dense. In this talk\, I w
ill present joint work with Finn Bartsch and Erwan Rousseau in which we sh
ow that the "transcendental-rational points" on the threefolds of Bogomolo
v-Tschinkel are not dense. \n\nhttps://events.dm.unipi.it/event/240/
LOCATION:Aula Seminari (Department of Mathematics)
URL:https://events.dm.unipi.it/event/240/
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