- abelian variety
- Математика: абелево многообразие
Универсальный англо-русский словарь. Академик.ру. 2011.
abelian variety
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Abelian variety — In mathematics, particularly in algebraic geometry, complex analysis and number theory, an Abelian variety is a projective algebraic variety that is at the same time an algebraic group, i.e., has a group law that can be defined by regular… … Wikipedia
Abelian variety of CM-type — In mathematics, an abelian variety A defined over a field K is said to have CM type if it has a large enough commutative subring in its endomorphism ring End(A). The terminology here is from complex multiplication theory, which was developed for… … Wikipedia
Dual abelian variety — In mathematics, a dual abelian variety can be defined from an abelian variety A, defined over a field K. Contents 1 Definition 2 History 3 Dual isogeny (elliptic curve case) … Wikipedia
Semistable abelian variety — In mathematics, a semistable abelian variety in Diophantine geometry is an abelian variety defined over a global or local field with reduction modulo all primes of restricted type.For an Abelian variety A defined over a field F with ring of… … Wikipedia
Conductor of an abelian variety — In mathematics, in Diophantine geometry, the conductor of an abelian variety defined over a local or global field F is a measure of how bad the bad reduction at some prime is. It is connected to the ramification in the field generated by the… … Wikipedia
Abelian — Abelian, in mathematics, is used in many different definitions, named after Norwegian mathematician Niels Henrik Abel:In group theory:*Abelian group, a group in which the binary operation is commutative **Category of abelian groups Ab has abelian … Wikipedia
Variety — may refer to: *Variety (botany), a rank in botany below that of species. *Variety (cybernetics), the number of possible states of a system or of an element of the system. *Variety (linguistics), a concept that includes for instance dialects,… … Wikipedia
Variety (universal algebra) — This article is about a class of algebraic structures of the same signature. For the set of solutions to a system of polynomial equations, see Algebraic variety. In mathematics, specifically universal algebra, a variety of algebras is the class… … Wikipedia
Abelian integral — In mathematics, an abelian integral in Riemann surface theory is a function related to the indefinite integral of a differential of the first kind. Suppose we are given a Riemann surface S and on it a differential 1 form ω that is everywhere… … Wikipedia
Arithmetic of abelian varieties — In mathematics, the arithmetic of abelian varieties is the study of the number theory of an abelian variety, or family of those. It goes back to the studies of Fermat on what are now recognised as elliptic curves; and has become a very… … Wikipedia
Equations defining abelian varieties — In mathematics, the concept of abelian variety is the higher dimensional generalization of the elliptic curve. The equations defining abelian varieties are a topic of study because every abelian variety is a projective variety. In dimension d ge; … Wikipedia
