WEIL NUMBERS GENERATED BY OTHER WEIL NUMBERS AND TORSION FIELDS OF ABELIAN VARIETIES
نویسندگان
چکیده
منابع مشابه
Weil Numbers Generated by Other Weil Numbers and Torsion Fields of Abelian Varieties
Using properties of the Frobenius eigenvalues, we show that, in a precise sense, “most” isomorphism classes of (principally polarized) simple abelian varieties over a finite field are characterized, up to isogeny, by the sequence of their division fields, and a similar result for “most” isogeny classes. Some global cases are also treated.
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متن کاملAbelian Varieties over Fields of Generated by Torsion Points
Let A be an abelian variety over a number field, T` the `adic Tate module, and G` the image of the Galois action on T`. Then H(G`, T`) is a finite `-group which vanishes for ` 0. We apply this bound for i = 1 and i = 2 to show that if K denotes the field generated by all torsion points of A, then A(K) is the direct sum of its torsion group and a free abelian group.
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2006
ISSN: 0024-6107,1469-7750
DOI: 10.1112/s0024610706023040