TY - JOUR
T1 - Points of small height on semiabelian varieties
AU - Kühne, Lars
N1 - Funding Information:
This work was supported by an Ambizione Grant of the Swiss National Science Founda-
PY - 2022/9/25
Y1 - 2022/9/25
N2 - The equidistribution conjecture is proved for general semiabelian varieties over number fields. Previously, this conjecture was only known in the special case of almost split semiabelian varieties through work of Chambert-Loir. The general case has remained intractable so far because the height of a semiabelian variety is negative unless it is almost split. In fact, this places the conjecture outside the scope of Yuan's equidistribution theorem on algebraic dynamical systems. To overcome this, an asymptotic adaption of the equidistribution technique invented by Szpiro, Ullmo, and Zhang is used here. It also allows a new proof of the Bogomolov conjecture and hence a self-contained proof of the strong equidistribution conjecture in the same general setting.
AB - The equidistribution conjecture is proved for general semiabelian varieties over number fields. Previously, this conjecture was only known in the special case of almost split semiabelian varieties through work of Chambert-Loir. The general case has remained intractable so far because the height of a semiabelian variety is negative unless it is almost split. In fact, this places the conjecture outside the scope of Yuan's equidistribution theorem on algebraic dynamical systems. To overcome this, an asymptotic adaption of the equidistribution technique invented by Szpiro, Ullmo, and Zhang is used here. It also allows a new proof of the Bogomolov conjecture and hence a self-contained proof of the strong equidistribution conjecture in the same general setting.
KW - Arakelov geometry
KW - arithmetic intersection theory
KW - Bogomolov conjecture
KW - equidistribution
KW - semiabelian varieties
KW - small height
UR - http://www.scopus.com/inward/record.url?scp=85128684562&partnerID=8YFLogxK
U2 - 10.4171/JEMS/1125
DO - 10.4171/JEMS/1125
M3 - Article
AN - SCOPUS:85128684562
VL - 24
SP - 2077
EP - 2131
JO - Journal of the European Mathematical Society
JF - Journal of the European Mathematical Society
SN - 1435-9855
IS - 6
ER -