Towards the Andre–Oort conjecture for mixed Shimura varieties: The Ax–Lindemann theorem and lower bounds for Galois orbits of special points

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

Autorschaft

  • Ziyang Gao

Organisationseinheiten

Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)85-146
FachzeitschriftJournal fur die Reine und Angewandte Mathematik
Jahrgang732
PublikationsstatusVeröffentlicht - 2017

Abstract

We prove in this paper the Ax-Lindemann-Weierstrass theorem for all mixed Shimura varieties and discuss the lower bounds for Galois orbits of special points of mixed Shimura varieties. In particular we reprove a result of Silverberg in a different approach. Then combining these results we prove the Andr\'e-Oort conjecture for any mixed Shimura variety whose pure part is a subvariety of A_6^n.

Zitieren

Towards the Andre–Oort conjecture for mixed Shimura varieties: The Ax–Lindemann theorem and lower bounds for Galois orbits of special points. / Gao, Ziyang.
in: Journal fur die Reine und Angewandte Mathematik, Jahrgang 732, 2017, S. 85-146.

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

Download
@article{5de0fcef05674e29818c143bf2ab0d51,
title = "Towards the Andre–Oort conjecture for mixed Shimura varieties: The Ax–Lindemann theorem and lower bounds for Galois orbits of special points",
abstract = " We prove in this paper the Ax-Lindemann-Weierstrass theorem for all mixed Shimura varieties and discuss the lower bounds for Galois orbits of special points of mixed Shimura varieties. In particular we reprove a result of Silverberg in a different approach. Then combining these results we prove the Andr\'e-Oort conjecture for any mixed Shimura variety whose pure part is a subvariety of A_6^n. ",
keywords = "math.AG, math.NT, 11G18, 11G15, 14G35, 14G05",
author = "Ziyang Gao",
year = "2017",
doi = "10.48550/arXiv.1310.1302",
language = "English",
volume = "732",
pages = "85--146",
journal = "Journal fur die Reine und Angewandte Mathematik",
issn = "0075-4102",
publisher = "Walter de Gruyter GmbH",

}

Download

TY - JOUR

T1 - Towards the Andre–Oort conjecture for mixed Shimura varieties

T2 - The Ax–Lindemann theorem and lower bounds for Galois orbits of special points

AU - Gao, Ziyang

PY - 2017

Y1 - 2017

N2 - We prove in this paper the Ax-Lindemann-Weierstrass theorem for all mixed Shimura varieties and discuss the lower bounds for Galois orbits of special points of mixed Shimura varieties. In particular we reprove a result of Silverberg in a different approach. Then combining these results we prove the Andr\'e-Oort conjecture for any mixed Shimura variety whose pure part is a subvariety of A_6^n.

AB - We prove in this paper the Ax-Lindemann-Weierstrass theorem for all mixed Shimura varieties and discuss the lower bounds for Galois orbits of special points of mixed Shimura varieties. In particular we reprove a result of Silverberg in a different approach. Then combining these results we prove the Andr\'e-Oort conjecture for any mixed Shimura variety whose pure part is a subvariety of A_6^n.

KW - math.AG

KW - math.NT

KW - 11G18, 11G15, 14G35, 14G05

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-84978366283&origin=inward&txGid=879cd787857f6556f1f7c3e8e21a8c48

U2 - 10.48550/arXiv.1310.1302

DO - 10.48550/arXiv.1310.1302

M3 - Article

VL - 732

SP - 85

EP - 146

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

SN - 0075-4102

ER -