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Results tagged with abelian-varieties
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user 16858
Abelian varieties are projective algebraic varieties endowed with an Abelian group structure. Over the complex numbers, they can be described as quotients of a vector space by a lattice of full rank. They are analogs in higher dimensions of elliptic curves, and play an important role in algebraic geometry and number theory.
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Weil pairing as an algebraic cycle?
Is there an algebraic cycle corresponding to the Weil pairing on an abelian variety (of dim>1)? Ideally I'd like to see an example as explicit as possible, e.g.
an explicitly given variety of dim>1 a …
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4
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Tate conjecture for abelian varieties over a finitely generated extension of an algebraicall...
Let $K$ be a finitely generated extension of an algebraically closed field of characteristic zero, and $A,B$ abelian varieties over $K$.
Then is $Hom_K(A,B)\otimes \mathbb{Z_l} \cong Hom_{Gal(\bar{K …
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Another question related to the isogeny theorem for elliptic curves
I was reading the following question: About isogeny theorem for elliptic curves and was interested in the following statement at the end of Torsten Ekedahl's answer:
"Note also that the situation is …
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2
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1
answer
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Serre's open image theorem for products of elliptic curves over function fields via speciali...
In Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math. 15, 259--331 (1972), Serre proved the following (Theorem 6
′′, p. 325):
Let $K$ be a number field and let
$K …
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6
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Mumford-Tate group and Galois representations
Could someone please point me towards a proof of why the image of a Galois representation on the Tate-module of an abelian variety is limited by its Mumford-Tate group?
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Modern proof of Serre's open image theorem?
Let $E$ be an elliptic curve defined over a number field $K$ without complex multiplication. Serre's open image theorem (which appears in his book 'Abelian $l$-Adic Representations and Elliptic Curves …
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