Roots of unity and torsion points of abelian varieties

被引：0

作者：

Lombardo, Davide ^{[1
]}

机构：

[1] Dept Math Orsay, F-91405 Orsay, France

来源：

RAMANUJAN JOURNAL | 2017年 / 43卷 / 02期

关键词：

Galois representations; Mumford-Tate conjecture; Abelian varieties; Algebraic cycles; CONJECTURE; FIELDS;

D O I：

10.1007/s11139-016-9813-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We answer a question raised by Hindry and Ratazzi concerning the intersection between cyclotomic extensions of a number field K and extensions of K generated by torsion points of an abelian variety over K. We prove that the property called in Hindry and Ratazzi (J Ramanujan Math Soc 25(1):81-111, 2010) holds for any abelian variety, while the same is not true for the stronger version of the property introduced in Hindry and Ratazzi (J Inst Math Jussieu 11(1):27-65, 2012).

引用

页码：383 / 403

页数：21

共 50 条

[21] Local-global properties of torsion points on three-dimensional abelian varieties
Cullinan, John
JOURNAL OF ALGEBRA, 2007, 311 (02) : 736 - 774
[22] Torsion for abelian varieties of type III
Farfan, Victoria Cantoral
JOURNAL OF NUMBER THEORY, 2019, 198 : 346 - 380
[23] THE DISTRIBUTION OF TORSION SUBSCHEMES OF ABELIAN VARIETIES
Achter, Jeffrey D.
JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2016, 15 (04) : 693 - 710
[24] ARITHMETIC OF ABELIAN VARIETIES WITH CONSTRAINED TORSION
Rasmussen, Christopher
Tamagawa, Akio
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 369 (04) : 2395 - 2424
[25] ENDOMORPHISMS AND TORSION OF ABELIAN-VARIETIES
ZARHIN, YG
DUKE MATHEMATICAL JOURNAL, 1987, 54 (01) : 131 - 145
[26] TORSION OF ABELIAN VARIETIES OF FINITE CHARACTERISTIC
ZARKHIN, YG
MATHEMATICAL NOTES, 1977, 22 (1-2) : 493 - 498
[27] Bounding the torsion in CM Abelian varieties
Ratazzi, Par Nicolas
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2007, 40 (06): : 951 - 983
[28] A BOUND FOR THE TORSION ON SUBVARIETIES OF ABELIAN VARIETIES
Galateau, Aurelien
Martinez, Cesar
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024, : 1693 - 1715
[29] CURVES ON AN ABELIAN VARIETY AND TORSION POINTS
RAYNAUD, M
INVENTIONES MATHEMATICAE, 1983, 71 (01) : 207 - 233
[30] Torsion points on abelian varieties of CM-type (vol 68, pg 241, 1988)
Silverberg, A.
COMPOSITIO MATHEMATICA, 2018, 154 (03) : 594 - 594

← 1 2 3 4 5 →