Endomorphisms and torsion of Abelian varieties

DOI10.1215/S0012-7094-87-05410-XzbMath0632.14035OpenAlexW2071435108MaRDI QIDQ1095214

Yuri G. Zarhin

Publication date: 1987

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-87-05410-x

zbMATH Keywords

solution of the torsion problem for abelian varieties

Mathematics Subject Classification ID

Algebraic theory of abelian varieties (14K05)

Related Items (17)

Abelian varieties over large algebraic fields with infinite torsion ⋮ Torsion of abelian varieties over GL(2)-extensions of number fields ⋮ Galois representations attached to elliptic curves with complex multiplication ⋮ On the properties of Northcott and Narkiewicz for elliptic curves ⋮ ON THE ESSENTIAL TORSION FINITENESS OF ABELIAN VARIETIES OVER TORSION FIELDS ⋮ Fine Selmer groups and ideal class groups ⋮ A generalization of a theorem of Imai and its applications to Iwasawa theory ⋮ A lower bound for the canonical height on elliptic curves over abelian extensions. ⋮ Abelian varieties over fields of finite characteristic ⋮ Cohomology and torsion cycles over the maximal cyclotomic extension ⋮ Selmer groups over \(\mathbb Z_p^d\)-extensions ⋮ The rank of abelian varieties over infinite Galois extensions ⋮ Acyclotomy of torsion in the CM case ⋮ On the Support Problem for Drinfeld Modules ⋮ Torsion points on elliptic curves over function fields and a theorem of Igusa ⋮ Abelian varieties over finitely generated fields and the conjecture of Geyer and Jarden on torsion ⋮ On the torsion points of Drinfeld modules in abelian extensions

Cites Work

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• A finiteness theorem for unpolarized Abelian varieties over number fields with prescribed places of bad reduction
• Finiteness theorems for abelian varieties over number fields.
• Torsion of Abelian varieties of finite characteristic.
• Good reduction of abelian varieties
• Rational points of Abelian varieties with values in towers of number fields
• Finiteness Problems in Diophantine Geometry
• A remark on the rational points of abelian varieties with values in cyclotomic $Z_p$-extensions
• Galois Action on Division Points of Abelian Varieties with Real Multiplications
• CYCLOTOMIC FIELDS AND MODULAR CURVES

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