## Details

Originalsprache | Englisch |
---|---|

Seiten (von - bis) | 2077-2131 |

Seitenumfang | 55 |

Fachzeitschrift | Journal of the European Mathematical Society |

Jahrgang | 24 |

Ausgabenummer | 6 |

Publikationsstatus | Veröffentlicht - 25 Sept. 2022 |

## Abstract

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.

## ASJC Scopus Sachgebiete

**Mathematik (insg.)**- Mathematik (insg.)
**Angewandte Mathematik**

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**Points of small height on semiabelian varieties.**/ Kühne, Lars.

in: Journal of the European Mathematical Society, Jahrgang 24, Nr. 6, 25.09.2022, S. 2077-2131.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

*Journal of the European Mathematical Society*, Jg. 24, Nr. 6, S. 2077-2131. https://doi.org/10.4171/JEMS/1125

*Journal of the European Mathematical Society*,

*24*(6), 2077-2131. https://doi.org/10.4171/JEMS/1125

}

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 -