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Results tagged with abelian-varieties
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user 6153
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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Terminology about Abelian varieties over finite fields
See http://en.wikipedia.org/wiki/Hasse-Witt_matrix#Abelian_varieties_and_their_p-rank . "Ordinary" is always defined by p-rank equal to the dimension (the maximum possible). The article gives one defi …
- 12.6k
17
votes
Why were Abelian functions so important in the 19th century?
Recall C. L. Siegel's rant, about the modern theory of abelian functions not having any functions in it.
From a point of view that would have made sense to Weierstrass, mathematics has "addition theo …
- 12.6k
2
votes
1
answer
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Weil reciprocity on abelian varieties and biextensions?
I was once told, by someone who would likely be right about such things, that the version of Weil reciprocity for abelian varieties (as in Lang, Abelian Varieties) should come out of consideration of …
- 12.6k