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Results tagged with abelian-varieties
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user 65
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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Why no abelian varieties over Z?
Comments by Anweshi
The essential point is what Emerton mentioned, ie the analogy with Minkowski's theorem on number fields with ramification. The basic principle is that "arithmetic is geometry". Nu …
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Examples of rational families of abelian varieties.
Just for the curiosity, into which category falls the fibration which has an elliptic curve with given j-invariant over a point $j \in \mathbb{P}^1$?
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5
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Why no abelian varieties over Z?
Motivation
I learned about this question from a wonderful article Rational points on curves by Henri Darmon. He gives a list of statements (some are theorems, some conjectures) of the form
the set $\ …
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Accepted
What is the Theorem of the Cube?
If you have a line bundle trivial on 3 "surfaces" of a "cube" $A\times B\times C$ where $A$, $B$, $C$ are abelian varieties, then this line bundle in trivial on the whole "cube".
See wikipedia.
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