ON THE TORSION ANOMALOUS CONJECTURE IN CM ABELIAN VARIETIES

被引:5
作者
Checcoli, Sara [1 ]
Viada, Evelina [2 ]
机构
[1] Univ Grenoble 1, Inst Fournier, F-38402 St Martin Dheres, France
[2] Univ Gottingen, Inst Math, D-37073 Gottingen, Germany
关键词
diophantine approximation; heights; abelian varieties; intersections with torsion varieties; SUBVARIETIES; BOUNDS;
D O I
10.2140/pjm.2014.271.321
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The torsion anomalous conjecture (TAC) states that a subvariety V of an abelian variety A has only finitely many maximal torsion anomalous subvarieties. In this work we prove, with an effective method, some cases of the TAC when the ambient variety A has CM, generalising our previous results in products of CM elliptic curves. When V is a curve, we give new results and we deduce some implications on the effective Mordell-Lang conjecture.
引用
收藏
页码:321 / 345
页数:25
相关论文
共 18 条
[1]   Anomalous Subvarieties-Structure Theorems and Applications [J].
Bombieri, E. ;
Masser, D. ;
Zannier, U. .
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2007, 2007
[2]  
Bombieri E., 1997, Ann. Scuola Norm. Sup. Pisa Cl. Sci., V23, P779
[3]   Petits points et multiplication complexe [J].
Carrizosa, Maria .
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2009, 2009 (16) :3016-3097
[4]  
CHECCOLI S, 2014, ATTI ACCAD NAZ LINCE, V25, P1
[5]  
Checcoli S, 2012, NEW YORK J MATH, V18, P891
[6]   Upper bounds of normalized heights of subvarieties of abelian varieties 2 [J].
David, S ;
Philippon, P .
COMMENTARII MATHEMATICI HELVETICI, 2002, 77 (04) :639-700
[7]   A minoration of the essential minimum on the varietes abeliennes [J].
Galateau, Aurelien .
COMMENTARII MATHEMATICI HELVETICI, 2010, 85 (04) :775-812
[8]  
Habegger P, 2008, MATH ANN, V342, P449, DOI 10.1007/s00208-008-0242-3
[9]   PERIODS AND MINIMAL ABELIAN SUBVARIETIES [J].
MASSER, D ;
WUSTHOLZ, G .
ANNALS OF MATHEMATICS, 1993, 137 (02) :407-458
[10]   Courbes algebriques et equations multiplicatives [J].
Maurin, Guillaume .
MATHEMATISCHE ANNALEN, 2008, 341 (04) :789-824