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Results tagged with abelian-varieties
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user 142444
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.
3
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Uniqueness of presentation for semi-abelian varieties
Let $k$ be any field and $G$ a semi-abelian variety over $k$, i.e., an algebraic group that fits into an exact sequence
$$ 1 \to T \to G \to A \to 1$$
of algebraic groups, where $T$ is an algebraic …
- 533
2
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0
answers
190
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Picard and Rosati for elliptic curves
I would like to ask for confirmation whether the following argument is correct.
We work over an algebraically closed field $k$ of characteristic $0$. For an elliptic curve $E$, the Picard variety, or …
- 533
1
vote
1
answer
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Cohomology of the dual Abelian variety
I am interested in the (degree $1$) Betti cohomology of the dual $A^\vee$ of an Abelian variety $A$ (say, over $\overline{\mathbb{Q}}$). We can even assume $A$ to be an elliptic curve, if this makes t …
- 533
1
vote
0
answers
131
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Polarization induces alternating pairing on homology
Let $A$ be an abelian variety over $\overline{\mathbb{Q}}$. We work up to isogeny (i.e., Hom sets are tensored with $\mathbb{Q}$). I am looking for a reference (and ideally, a short explanation) for t …
- 533