In algebraic geometry, the function field of an algebraic variety V consists of objects that are interpreted as rational functions on V. In classical...
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of an algebraic function field is not a well-defined notion. The algebraic function fields over k form a category; the morphisms from function field K...
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Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as...
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used in algebraic geometry. There the function field of an algebraic variety V is formed as the field of fractions of the coordinate ring of V (more accurately...
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In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials. It is also called...
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specifically in algebraic geometry, the dimension of an algebraic variety may be defined in various equivalent ways. Some of these definitions are of geometric...
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The sheaf of rational functions KX of a scheme X is the generalization to scheme theory of the notion of function field of an algebraic variety in classical...
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fields: Algebraic number field: A finite extension of Q {\displaystyle \mathbb {Q} } Global function field: The function field of an irreducible algebraic curve...
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mathematics, an algebraic structure or algebraic system consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations...
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projective plane of a homogeneous polynomial in three variables. An affine algebraic plane curve can be completed in a projective algebraic plane curve by...
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real numbers. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics. The...
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Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems...
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In the mathematical field of algebraic geometry, a singular point of an algebraic variety V is a point P that is 'special' (so, singular), in the geometric...
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Function field may refer to: Function field of an algebraic variety Function field (scheme theory) Algebraic function field Function field sieve Function...
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Spaltenstein variety Arithmetic genus, geometric genus, irregularity Tangent space, Zariski tangent space Function field of an algebraic variety Ample line...
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in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a smooth projective algebraic variety that is also an algebraic...
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In algebraic geometry, an affine algebraic set is the set of the common zeros over an algebraically closed field k of some family of polynomials in the...
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universal algebra, a variety of algebras or equational class is the class of all algebraic structures of a given signature satisfying a given set of identities...
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mathematics, a rational variety is an algebraic variety, over a given field K, which is birationally equivalent to a projective space of some dimension over...
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algebra, an adelic algebraic group is a semitopological group defined by an algebraic group G over a number field K, and the adele ring A = A(K) of K...
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Scheme (mathematics) (redirect from Scheme (algebraic geometry))
specifically algebraic geometry, a scheme is a structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities...
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the Hasse–Weil zeta function attached to an algebraic variety V defined over an algebraic number field K is a meromorphic function on the complex plane...
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In algebraic geometry, divisors are a generalization of codimension-1 subvarieties of algebraic varieties. Two different generalizations are in common...
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projective algebraic variety over the field Fq with q elements and Nk is the number of points of V defined over the finite field extension Fqk of Fq. Making...
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Local ring (redirect from Local ring of a variety)
sense of functions defined on algebraic varieties or manifolds, or of algebraic number fields examined at a particular place, or prime. Local algebra is...
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used for the study of algebraic varieties, which are solution sets of systems of polynomial equations. Weyl algebras and Lie algebras may be considered...
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Separable extension (redirect from Separable algebraic extension)
In field theory, a branch of algebra, an algebraic field extension E / F {\displaystyle E/F} is called a separable extension if for every α ∈ E {\displaystyle...
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Diophantine equations and are typically functions from a set of points on algebraic varieties (or a set of algebraic varieties) to the real numbers. For instance...
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function defined on M. More generally, given an algebraic variety V over some field K, the function field K(V), consisting of the rational functions defined...
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in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function fields. These properties...
40 KB (5,798 words) - 23:17, 22 December 2024