Equations defining abelian varieties information

the concept of abelian variety is the higher-dimensional generalization of the elliptic curve. The equations defining abelian varieties are a topic of...

number theory. An abelian variety can be defined by equations having coefficients in any field; the variety is then said to be defined over that field....

projective space. See equations defining abelian varieties); thus, Jac ⁡ ( C ) {\displaystyle \operatorname {Jac} (C)} is a projective variety. The tangent space...

abelian varieties Duality of abelian varieties c.1967 David Mumford develops a new theory of the equations defining abelian varieties 1968 Serre–Tate theorem...

varieties. The actual projective embeddings are complicated (see equations defining abelian varieties) when n > 1, and are really coextensive with the theory of...

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...

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...

Another class is formed by the abelian varieties, which are the algebraic groups whose underlying variety is a projective variety. Chevalley's structure theorem...

Let K be a field over which the curve is defined (that is, the coefficients of the defining equation or equations of the curve are in K) and denote the curve...

differential equations. Many of the equations of the mathematical physics of the nineteenth century can be treated this way. Fourier studied the heat equation, which...

variety has no defining set of equations that is so transparent. Detailed studies, for example of canonical curves and the equations defining abelian...

In mathematics, a free abelian group is an abelian group with a basis. Being an abelian group means that it is a set with an addition operation that is...

Geometric Invariant Theory, on the equations defining an abelian variety, and on algebraic surfaces. His books Abelian Varieties (with C. P. Ramanujam) and Curves...

"Prym varieties". Complex Abelian Varieties. New York: Springer-Verlag. pp. 363–410. ISBN 3-540-20488-1. Mumford, David (1974), "Prym varieties. I", in...

has dimension g. Varieties, such as the Jacobian variety, which are complete and have a group structure are known as abelian varieties, in honor of Niels...

Mumford for discrete Heisenberg groups, in his theory of equations defining abelian varieties. This is a large generalization of the approach used in Jacobi's...

{\displaystyle n-1.\ } Fermat-style equations in more variables define as projective varieties the Fermat varieties. Baker, Matthew; Gonzalez-Jimenez,...

algebraic varieties, can be understood by studying the possible nice shapes sitting inside those spaces, which look like zero sets of polynomial equations. The...

algebraic varieties, singularities, moduli, and formal moduli. An important class of varieties, not easily understood directly from their defining equations, are...

group is non-commutative, then the gauge theory is referred to as non-abelian gauge theory, the usual example being the Yang–Mills theory. Many powerful...

primes'. Arithmetic of abelian varieties See main article arithmetic of abelian varieties Artin L-functions Artin L-functions are defined for quite general...

contained in the concept of abelian variety, or more precisely in the way an algebraic curve can be mapped into abelian varieties. Abelian integrals were later...

solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently, a solvable group is a group whose...

Alternatively, they may be described by polynomial equations, in which case they are called algebraic varieties, and if they additionally carry a group structure...

any non-abelian gauge theory, any maximal abelian gauge is an incomplete gauge which fixes the gauge freedom outside of the maximal abelian subgroup...

If G and H are abelian (i.e., commutative) groups, then the set Hom(G, H) of all group homomorphisms from G to H is itself an abelian group: the sum h...

ways. Abelian varieties have been introduced above. The presence of the group operation yields additional information which makes these varieties particularly...