mathematics, a dual abelian variety can be defined from an abelian variety A, defined over a field k. A 1-dimensional abelian variety is an elliptic curve...

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...

mathematics, the arithmetic of abelian varieties is the study of the number theory of an abelian variety, or a family of abelian varieties. It goes back to the...

This is a timeline of the theory of abelian varieties in algebraic geometry, including elliptic curves. c. 1000 Al-Karaji writes on congruent numbers...

there is a similar Weil pairing between points of order n of an abelian variety and its dual. It was introduced by André Weil (1940) for Jacobians of curves...

Dual abelian variety Dual basis Dual (category theory) Dual code Duality (electrical engineering) Duality (optimization) Dualizing module Dualizing sheaf...

component of the identity in the Picard group of C, hence an abelian variety. The Jacobian variety is named after Carl Gustav Jacobi, who proved the complete...

In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements...

Groot dual Dual abelian variety Dual basis in a field extension Dual bundle Dual curve Dual (category theory) Dual graph Dual group Dual object Dual pair...

conventionally spelled with a lower-case initial "a" (e.g., abelian group, abelian category, and abelian variety). On 6 April 1929, four Norwegian stamps were issued...

involving the dual abelian variety A ^ {\displaystyle {\hat {A}}} . Elliptic curves as 1-dimensional abelian varieties are their own duals, i.e. E ^ = E...

On the other hand, an abelian scheme may not be projective. Examples of abelian varieties are elliptic curves, Jacobian varieties and K3 surfaces. Let...

polarized complex abelian varieties of dimension g {\displaystyle g} (a principal polarization identifies an abelian variety with its dual). The theory of...

important step in algebraic geometry, in particular in the duality theory of abelian varieties. It was constructed by Grothendieck (1962), and also described...

The toric variety of the polytope is the toric variety of its fan. A variation of this construction is to take a rational polytope in the dual of N and...

variety of a curve. The Albanese variety is the abelian variety A {\displaystyle A} generated by a variety V {\displaystyle V} taking a given point of V...

A/K be an abelian variety, let B ≅ Pic0(A) be the dual abelian variety to A, and let P be the Poincaré line bundle on A × B. Then the abelian regulator...

Abelian integral Abelian surface Abelian variety Abelian variety of CM-type Dual abelian variety Abelian von Neumann algebra Abeltoppen, a mountain in Dickson...

equivalence between the derived categories of coherent sheaves on an abelian variety and its dual. That equivalence is analogous to the classical Fourier transform...

\mathbb {Z} ).} However, we note that the dual is not considered just as an abstract Abelian group of functionals, but comes with a natural inner...

algebraic groups (also known as group varieties) that is surjective and has a finite kernel. If the groups are abelian varieties, then any morphism f : A → B of...

conjecture holds for sufficiently general abelian varieties, for products of elliptic curves, and for simple abelian varieties of prime dimension. However, Mumford...

Complete group varieties are called abelian varieties. This generalizes to the notion of abelian scheme; a group scheme G over a base S is abelian if the structural...

to be an algebraic variety; those that are varieties can be embedded into complex projective space, and are the abelian varieties. The actual projective...

In mathematics, a Tate module of an abelian group, named for John Tate, is a module constructed from an abelian group A. Often, this construction is made...

an abelian variety, Y its dual abelian variety. Then Db(Coh(X)) is equivalent to Db(Coh(Y)) by the theory of Fourier–Mukai transforms. Varieties with...

generalizations. For smooth manifolds, Alexander duality is a formal consequence of Verdier duality for sheaves of abelian groups. More precisely, if we let X {\displaystyle...

see Appendix B Faltings, Gerd; Chai, Ching-Li. Degeneration of abelian varieties. With an appendix by David Mumford. Springer-Verlag, Berlin, 1990...

twisted Poincaré duality. Blanchfield duality is a version of Poincaré duality which provides an isomorphism between the homology of an abelian covering space...

0 ( A ) {\displaystyle {\hat {A}}=\mathrm {Pic} ^{0}(A)} be the dual abelian variety, and for a ∈ A {\displaystyle a\in A} , let T a : A → A {\displaystyle...