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...

context of connected smooth linear algebraic group. pure dimension A scheme has pure dimension d if each irreducible component has dimension d. quasi-coherent...

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

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

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...

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 K/k(x)} . The dimension of a scheme of finite type over a field is equal to the transcendence degree of the residue field of the generic point. Arithmetic...

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...

11th Dimension is the second studio album by American rapper Ski Mask the Slump God. It was released through Victor Victor, Republic Records, and UMG...

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

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

scheme, for example a smooth variety over a field, is Cohen–Macaulay. Any 0-dimensional ring (or equivalently, any Artinian ring). Any 1-dimensional reduced...

Annie in a scheme to force Dai to reveal the meaning behind the Nazca images. After saving Annie, Shaider chases Mumu into the Fushigi Dimension and manages...

is an affine scheme (except for zero-dimensional projective spaces). Projective schemes, meaning those that arise as closed subschemes of a projective space...

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...

fields, a kinetic scheme is a network of states and connections between them representing a dynamical process. Usually a kinetic scheme represents a Markovian...

algebraic geometry, a scheme is a structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the...

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

a cycle of codimension 1. A Riemann surface is a 1-dimensional complex manifold, and so its codimension-1 submanifolds have dimension 0. The group of...

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...

projective space of a Zariski-open and a Zariski-closed subset. A similar definition is used in scheme theory, where a quasi-projective scheme is a locally closed...

thickening of metal rails, original glazing and light switches replaced by standard 21st-century products, a stair clumsily misplaced and mis-dimensioned, a colour...

algebraic varieties of dimension two are called algebraic surfaces. In the context of modern scheme theory, an algebraic variety over a field is an integral...

schemes as well. Mobile deep links are one example of a class of unofficial URI schemes that allow for linking directly to a specific location in a mobile...

of Y by induction on the dimension, then eliminate the singularities in the fibers. It is easy to extend the definition of resolution to all schemes....

case: the ring of regular functions on a proper scheme X over a field k has finite dimension as a k-vector space. By contrast, the ring of regular functions...

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...

The highway dimension is a graph parameter modelling transportation networks, such as road networks or public transportation networks. It was first formally...

V) of a vector space V over a field F is the moduli space of all k-dimensional linear subspaces of V. Whenever there is an embedding of a scheme X {\displaystyle...