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The uniform Bogomolov conjecture for algebraic curves
2.12.2021, 16:15 - 17:15
Speaker:Lars Kühne, University of Copenagen
Location:Anderer Ort/Other LocationZoom:
Organizer:Mathematisches Institut
I will present an equidistribution result for families of (non-degenerate) subvarieties in a family of abelian varieties. Using this result,
one can deduce a uniform version of the classical Bogomolov conjecture for curves embedded in their Jacobians, namely that the
number of torsion points lying on them is uniformly bounded in the genus of the curve. This has been previously only known in a few
select cases by work of David–Philippon and DeMarco–Krieger–Ye. Furthermore, one can deduce a rather uniform version of the
Mordell conjecture by complementing a result of Dimitrov–Gao–Habegger: The number of rational points on a smooth algebraic curve
defined over a number field can be bounded solely in terms of its genus and the Mordell-Weil rank of its Jacobian. Again, this was
previously known only under additional assumptions (Stoll, Katz–Rabinoff–Zureick–Brown). All these results have been recently
generalized beyond curves in joint work with Ziyang Gao and Tangli Ge, but the talk will focus on the simpler case of curves.
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