Concept information
Preferred term
abelian variety
Definition
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In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions. Abelian varieties are at the same time among the most studied objects in algebraic geometry and indispensable tools for much research on other topics in algebraic geometry and number theory.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Abelian_variety)
Broader concept
Narrower concepts
- abelian integral
- abelian surface
- arithmetic of abelian varieties
- Bogomolov conjecture
- complex multiplication
- conductor of an abelian variety
- Fay's trisecant identity
- height function
- height zeta function
- Jacobian variety
- Mordell-Weil group
- Mordell-Weil theorem
- Prym variety
- semistable abelian variety
- torsion conjecture
In other languages
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French
URI
http://data.loterre.fr/ark:/67375/PSR-H3Z5XWTH-5
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