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Results tagged with abelian-varieties
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user 8621
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.
7
votes
Example of non-modular elliptic surface?
The modular elliptic surfaces are quite rare. E.g., the Mordell-Weil group is finite and the Picard number of the surface equals $h^{1,1}$ (see Shioda's paper). Such elliptic surfaces are called extre …
- 3,338
5
votes
Accepted
Selmer of an abelian variety versus that of its dual.
Let $\varphi:A\to A^t$ be a polarization. Then $\varphi$ is an isogeny.
In order to study the difference between the Selmer groups of $A$ and of $A^t$ you need to study the torsion subgroups of $A(K)$ …
- 3,338