Dimension of a scheme information

geometry, the dimension of a scheme is a generalization of a dimension of an algebraic variety. Scheme theory emphasizes the relative point of view and, accordingly...

glossary of arithmetic and Diophantine geometry. For simplicity, a reference to the base scheme is often omitted; i.e., a scheme will be a scheme over some...

algorithm to compute its real dimension. Dimension (vector space) Dimension theory (algebra) Dimension of a scheme Chapter 11 of Atiyah, Michael Francis; Macdonald...

xn]. The affine scheme X is smooth of dimension m over k if X has dimension at least m in a neighborhood of each point, and the matrix of derivatives (∂gi/∂xj)...

{\displaystyle t} dimension and i {\displaystyle i} refers to the x {\displaystyle x} dimension. (By comparison, a central difference scheme in this scenario...

harmonics) up to a given order, leading to a sequence of increasingly dense grids analogous to the one-dimensional Gauss-Legendre scheme. The Lebedev grid...

geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space (or a more general...

A morphism Spec(K) → X, K some field, is equivalent to giving a point x ∈ X and an extension K/k(x). The dimension of a scheme of finite type over a field...

relative dimension g is a proper, smooth group scheme over S whose geometric fibers are connected and of dimension g. The fibers of an abelian scheme are abelian...

non-archimedean local field, K, is an extension of the Weil group WK by a one-dimensional additive group scheme Ga, introduced by Deligne (1973, 8.3.6). In...

dimension one (curves) are schemes. Non-singular proper algebraic spaces of dimension two over a field (smooth surfaces) are schemes. Quasi-separated group...

Krull dimension of a commutative ring R, named after Wolfgang Krull, is the supremum of the lengths of all chains of prime ideals. The Krull dimension need...

"integral".) The normalization of a scheme of dimension 1 is regular, and the normalization of a scheme of dimension 2 has only isolated singularities...

\operatorname {Spec} } yields a contravariant equivalence between the category of commutative rings and the category of affine schemes; each of these categories is...

projective surface if its dimension is two; it is a projective hypersurface if its dimension is one less than the dimension of the containing projective...

fundamental group scheme is a group scheme canonically attached to a scheme over a Dedekind scheme (e.g. the spectrum of a field or the spectrum of a discrete...

optional 2-dimensional, 7-pass interlacing scheme—the Adam7 algorithm. This is more sophisticated than GIF's 1-dimensional, 4-pass scheme, and allows a clearer...

In color theory, a color scheme is a combination of 2 or more colors used in aesthetic or practical design. Aesthetic color schemes are used to create...

quantum field theory, the minimal subtraction scheme, or MS scheme, is a particular renormalization scheme used to absorb the infinities that arise in perturbative...

using the 'geo' scheme name. A 'geo' URI identifies a physical location in a two- or three-dimensional coordinate reference system in a compact, simple...

general, the multiplicity of this product (i.e., the dimension of the scheme) is called the rank of the torus, and it is a locally constant function on...

every affine scheme X of finite type over a field k has a finite surjective morphism to affine space An over k, where n is the dimension of X. Likewise...

scheme over a field, and its properties are much the same as in the special case of smooth schemes. For a Gorenstein scheme X of finite type over a field...