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Concept in algebraic geometry
algebraic geometry, a smooth scheme over a field is a scheme which is well approximated by affine space near any point. Smoothness is one way of making
Smooth_scheme
regular scheme is a locally Noetherian scheme whose local rings are regular everywhere. Every smooth scheme is regular, and every regular scheme of finite
Regular_scheme
following case: suppose we have an embedding of a scheme X {\displaystyle X} into a smooth scheme Y {\displaystyle Y} i : X ↪ Y {\displaystyle i:X\hookrightarrow
Virtual_fundamental_class
geometry, a morphism f : X → S {\displaystyle f:X\to S} between schemes is said to be smooth if (i) it is locally of finite presentation (ii) it is flat,
Smooth_morphism
Construct in algebraic geometry
differentials. Let i : X → Y {\displaystyle i:X\to Y} be a closed embedding of smooth schemes in Sch / S {\displaystyle {\text{Sch}}/S} . Using the exact triangle
Cotangent_complex
Degree of differentiability of a function or map
analysis, the smoothness describes the number of times a function can be differentiated without producing discontinuities. The smoothness, or differentiability
Smoothness
Type of mathematical object
that all algebraic groups have group scheme structure, but group schemes are not necessarily connected, smooth, or defined over a field. This extra generality
Group_scheme
Application of homotopy to algebraic varieties
functor from the category S m S {\displaystyle Sm_{S}} of smooth S {\displaystyle S} -schemes towards an infinity category which satisfies Nisnevich descent
A¹_homotopy_theory
Algebraic geometry scheme
properties are much the same as in the special case of smooth schemes. For a Gorenstein scheme X of finite type over a field, f: X → Spec(k), the dualizing
Gorenstein_scheme
Weil cohomology theory for schemes X over a base field k
cohomology only works well for smooth proper schemes. Rigid cohomology extends it to more general schemes. For schemes in characteristic p, crystalline
Crystalline_cohomology
Point without a tangent space
point is said to be non-singular or smooth. The concept is generalized to smooth schemes in the modern language of scheme theory. A plane curve defined by
Singular point of an algebraic variety
Singular_point_of_an_algebraic_variety
Levine. In more precise terms, a theorem of Voevodsky implies: for a smooth scheme X over a field and integers p, q, there is a natural isomorphism H p
Bloch's_higher_Chow_group
Invariant of algebraic varieties and of more general schemes
(i))} when X is smooth over k. The motivic cohomology H i ( X , Z ( j ) ) {\displaystyle H^{i}(X,\mathbb {Z} (j))} of a smooth scheme X over k is the
Motivic_cohomology
is a scheme X that is locally of finite type and regular over k. 3. A smooth scheme over a field k is a scheme X that is geometrically smooth: X × k
Glossary of algebraic geometry
Glossary_of_algebraic_geometry
Fitting an approximating function to data
In statistics and image processing, to smooth a data set is to create an approximating function that attempts to capture important patterns in the data
Smoothing
generated k-algebra A is 0-smooth over k if and only if Spec A is a smooth scheme over k. A separable algebraic field extension L of k is 0-étale over
Smooth_algebra
Analogs of homology groups for algebraic varieties
When X {\displaystyle X} is smooth over k {\displaystyle k} (or more generally, a locally Noetherian normal factorial scheme ), this is isomorphic to the
Chow_group
Theorem in algebraic geometry
version works for schemes with mild singularities, Cohen–Macaulay schemes, not just smooth schemes. Namely, for a Cohen–Macaulay scheme X of pure dimension
Serre_duality
Mathematical theory
comparison isomorphisms in arithmetic and complex geometry: If X is a proper smooth scheme over C, there is a classical comparison isomorphism between the algebraic
P-adic_Hodge_theory
Meromorphic differential form
p-forms Ω X p ( log D ) {\displaystyle \Omega _{X}^{p}(\log D)} on a smooth scheme X over a field, with respect to a divisor D = ∑ D j {\displaystyle D=\sum
Logarithmic_form
Suppose that X {\displaystyle X} is a reduced closed subscheme of a smooth scheme Y {\displaystyle Y} . Take a log resolution π : Z → Y {\displaystyle
Du_Bois_singularity
Theorem in geometry
embedding X ↪ P {\displaystyle X\hookrightarrow P} into a smooth scheme P followed by a smooth morphism P → Y {\displaystyle P\to Y} , then let T f = [
Riemann–Roch-type_theorem
Moduli scheme of subschemes of a scheme, represents the flat-family-of-subschemes functor
of smooth curves in the Hilbert scheme. "Hilbert scheme" sometimes refers to the punctual Hilbert scheme of 0-dimensional subschemes on a scheme. Informally
Hilbert_scheme
Choice of colors used in design
discrete or continuous: Continuous: Color schemes that have a smooth color gradient. Continuous color schemes are intended to display sets of continuous
Color_scheme
Branch of mathematics
to algebraic vector bundles over a smooth scheme. But, there is an alternative construction for any Noetherian scheme X {\displaystyle X} . If we look at
K-theory
Generalization of vector bundles
rank n {\displaystyle n} . If Y {\displaystyle Y} is a smooth closed subscheme of a smooth scheme X {\displaystyle X} over k {\displaystyle k} , then there
Coherent_sheaf
Type of functor
to be smooth of dimension n - j if there is a smooth presentation U → X {\displaystyle U\to X} of relative dimension j for some smooth scheme U of dimension
Morphism_of_algebraic_stacks
presheaf F with transfers is restricted to the subcategory of smooth separated schemes, it can be viewed as a presheaf on the category with extra maps
Presheaf_with_transfers
Algebraic variety in a projective space
generalization to projective, but not necessarily smooth schemes is known as Verdier duality. For a (smooth projective) curve X, H2 and higher vanish for
Projective_variety
Generalization of algebraic variety
In mathematics, specifically algebraic geometry, a scheme is a structure that enlarges the notion of an algebraic variety in several ways, such as taking
Scheme_(mathematics)
Counterexample in algebraic geometry
gives an example of a smooth complete variety whose Hilbert scheme does not exist. Grothendieck showed that the Hilbert scheme always exists for projective
Hironaka's_example
Differential algebra
D_{\mathbb {A} _{R}^{n}/R}} . More generally, let X {\displaystyle X} be a smooth scheme over a ring R {\displaystyle R} . Locally, X → R {\displaystyle X\to
Weyl_algebra
Construction in algebraic geometry
descent results mentioned imply that a scheme X over k is smooth over k if and only if the base change XE is smooth over E. The same goes for properness
Fiber_product_of_schemes
scheme Scheme Éléments de géométrie algébrique Grothendieck's Séminaire de géométrie algébrique Fiber product of schemes Flat morphism Smooth scheme Finite
List of algebraic geometry topics
List_of_algebraic_geometry_topics
Result in algebraic geometry
where f is a proper map between two smooth schemes. Generalisations of the theorem can be made to the non-smooth case by considering an appropriate generalisation
Grothendieck–Riemann–Roch theorem
Grothendieck–Riemann–Roch_theorem
necessary condition for a scheme to be embedded into a smooth variety (or more generally a separated Noetherian regular scheme). To an extent, it is also
Divisorial_scheme
Method of hydrodynamics simulation
Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid
Smoothed-particle hydrodynamics
Smoothed-particle_hydrodynamics
Scheme used in the numerical solution of partial differential equations
fifth order accurate WENO scheme, whilst higher order schemes can be used where the problem demands improved accuracy in smooth regions. The method of holistic
High-resolution_scheme
Streaming media technique
standard. Microsoft provided Smooth Streaming Client software development kits for Silverlight and Windows Phone 7, as well as a Smooth Streaming Porting Kit
Adaptive_bitrate_streaming
In algebraic geometry, the Hurwitz scheme H d , g {\displaystyle {\mathcal {H}}_{d,g}} is the scheme parametrizing pairs ( C , π : C → P 1 {\displaystyle
Hurwitz_scheme
λ-operators. If we have a short exact sequence of vector bundles over a smooth scheme X {\displaystyle X} 0 → E ″ → E → E ′ → 0 , {\displaystyle 0\to {\mathcal
Λ-ring
Estimate of the importance of a word in a document
digital libraries used tf–idf.[verify] Variations of the tf–idf weighting scheme were often used by search engines as a central tool in scoring and ranking
Tf–idf
Type of object in algebraic geometry
admits an étale surjective atlas by a scheme. If, in the definition above, the word “étale” is weakened to “smooth”, one obtains the notion of an algebraic
Deligne–Mumford_stack
Singularities of algebraic varieties
language of schemes, transversality means that the scheme-theoretic intersection of any s of the D j {\displaystyle D_{j}} 's is smooth of codimension
Normal_crossing_singularity
Curved curface derived from a coarse polygon mesh
noticed that the butterfly scheme cannot generate smooth surfaces for irregular triangle meshes and thus modified this scheme. Kobbelt (1996) further generalized
Subdivision_surface
their speed and teamwork to clinch the win. Hanz and Dak have an equally smooth run in C Block, securing their place in the final. There, they face off
List of Danball Senki episodes
List_of_Danball_Senki_episodes
Lisp dialect
language. The Racket language is a modern dialect of Lisp and a descendant of Scheme. It is designed as a platform for programming language design and implementation
Racket_(programming_language)
Geometric space whose points represent algebro-geometric objects of some fixed kind
Consequently, the moduli space of smooth curves and linear systems (satisfying certain criteria) may be embedded in the Hilbert scheme of a sufficiently high-dimensional
Moduli_space
Vector bundle of cotangent spaces at every point in a manifold
structure than smooth manifolds, such as complex manifolds, or (in the form of cotangent sheaf) algebraic varieties or schemes. In the smooth case, any Riemannian
Cotangent_bundle
Element of Japanese language
had been organized since prehistoric times according to the same organic scheme as the Americans: gens, phratry, tribe, league of tribes. The phratry may
Japanese conjugation (ren'yōkei base)
Japanese_conjugation_(ren'yōkei_base)
History of maths
relative point of view, S-schemes. 1957 Alexander Grothendieck Grothendieck–Hirzebruch–Riemann–Roch theorem for smooth schemes; the proof introduces K-theory
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
Algorithm to smooth a polygonal mesh
Laplacian smoothing is an algorithm to smooth a polygonal mesh. For each vertex in a mesh, a new position is chosen based on local information (such as
Laplacian_smoothing
Mathematical model
that AK is a smooth separated scheme over K (such as an abelian variety). Then a Néron model of AK is defined to be a smooth separated scheme AR over R with
Néron_model
among others. The idea is to study some algebraic variety (or scheme) U which is smooth but not necessarily proper by embedding it into X, which is proper
Log_structure
Generalisation of a sheaf; a fibered category that admits effective descent
X {\displaystyle X} is a scheme ( S c h / S ) {\displaystyle (Sch/S)} and G {\displaystyle G} is a smooth affine group scheme acting on X {\displaystyle
Stack_(mathematics)
Any small, fluid-filled, spherical organelle enclosed by a membrane
Scheme of a liposome formed by phospholipids in an aqueous solution[further explanation needed]
Vesicle (biology and chemistry)
Vesicle_(biology_and_chemistry)
In algebraic geometry, a derived scheme is a homotopy-theoretic generalization of a scheme in which classical commutative rings are replaced with derived
Derived_scheme
Episodes of the American sitcom
and George is a bundle of nerves. Despite that, the wedding comes off smoothly. But when Georgiana and Bob drive off, Dennis is in the back seat of their
List of Dennis the Menace (1959 TV series) episodes
List_of_Dennis_the_Menace_(1959_TV_series)_episodes
Type of commutative ring in mathematics
K[[x_{1},\ldots ,x_{n}]]} . In geometric terms, every regular scheme, for example a smooth variety over a field, is Cohen–Macaulay. Any 0-dimensional ring
Cohen–Macaulay_ring
Type of numerical integration
traditional algorithms may fail. Adaptive quadrature follows the general scheme 1. procedure integrate ( f, a, b, τ ) 2. Q ≈ ∫ a b f ( x ) d x {\displaystyle
Adaptive_quadrature
Moduli space in the category of schemes
the existence of a coarse moduli scheme. Mumford proved that if g > 1, there exists a coarse moduli scheme of smooth curves of genus g, which is quasi-projective
Moduli_scheme
German breed of dog
German breed of short-legged, long-bodied dog of hound type. It may be smooth-haired, wire-haired, or long-haired, in various colors. It was bred to scent
Dachshund
Generalization of the Bernoulli process to more than two possible outcomes
the Bernoulli scheme or Bernoulli shift is a generalization of the Bernoulli process to more than two possible outcomes. Bernoulli schemes appear naturally
Bernoulli_scheme
more, telling him to never set foot in the station again. Bayleaf tries to smooth things, but Donalds runs away. He goes playing with his model fire station
List of London's Burning episodes
List_of_London's_Burning_episodes
Mathematical descriptions of molecular diffusion
The solute appears to move smoothly and systematically from high-concentration areas to low-concentration areas. This smooth flow is described by Fick's
Fick's_laws_of_diffusion
Concept in algebraic geometry
In algebraic geometry, a morphism of schemes generalizes a morphism of algebraic varieties just as a scheme generalizes an algebraic variety. It is, by
Morphism_of_schemes
formally smooth. Hence formal smoothness is a slight generalization of smooth morphisms. One method for detecting formal smoothness of a scheme is using
Formally_smooth_map
Manifold upon which it is possible to perform calculus
map is smooth, and every smooth map is Ck for any k, one can see that any analytic atlas can also be viewed as a smooth atlas, and every smooth atlas can
Differentiable_manifold
Projective variety that is also an algebraic group
of abelian varieties. An abelian scheme over a base scheme S of relative dimension g is a proper, smooth group scheme over S whose geometric fibers are
Abelian_variety
Mathematical group occurring in algebraic geometry and the theory of complex manifolds
→S be a morphism of schemes. The relative Picard functor (or relative Picard scheme if it is a scheme) is given by: for any S-scheme T, Pic X / S ( T
Picard_group
The Semi-Lagrangian scheme (SLS) is a numerical method that is widely used in numerical weather prediction models for the integration of the equations
Semi-Lagrangian_scheme
Mathematical construction
of this sheaf are injective!) In contrast, for the sheaf of smooth functions on a smooth manifold, germs contain some local information, but are not enough
Stalk_(sheaf)
In algebraic geometry, given a morphism of schemes p : X → S {\displaystyle p:X\to S} , the diagonal morphism δ : X → X × S X {\displaystyle \delta :X\to
Diagonal morphism (algebraic geometry)
Diagonal_morphism_(algebraic_geometry)
Completed: Engine fully rebuilt with oversized pistons, re-bored block, and smoothed crankshaft, non-original rear axle replaced with original part, clutch
List of Wheeler Dealers episodes
List_of_Wheeler_Dealers_episodes
of coarse rope would be rolled up and run around the rope for a final smoothing and polishing. The produced ropes would then be safely stored, thus creating
History_of_cannabis_in_Italy
Road pricing scheme in Singapore
The Singapore Area Licensing Scheme (ALS) was a road pricing scheme introduced in Singapore from 1975 to 1998 that charged drivers who were entering downtown
Area_Licensing_Scheme
senior-living community between recent newcomer Lena Driskell, 78, and smooth-talking grandfather Herman Winslow, 85, but Herman's charisma is well known
List_of_Deadly_Women_episodes
Batista thanked them for their work, and praised the executives for the smooth success of the conference. President Batista offered his congratulations
Freemasonry_in_Cuba
Property of certain numerical methods
linear schemes which preserve monotonicity are, at most, only first order accurate. Higher order linear schemes, although more accurate for smooth solutions
Total_variation_diminishing
Finite volume method in partial differential equations
the above second-order scheme provides greater accuracy for smooth solutions, it is not a total variation diminishing (TVD) scheme and introduces spurious
MUSCL_scheme
correspondences topologically. Smooth topology Uses smooth morphisms, but is usually equivalent to the etale topology (at least for schemes). Canonical topology
List of topologies on the category of schemes
List_of_topologies_on_the_category_of_schemes
Fiber bundle whose fibers are projective spaces
_{U}^{n}} and transition automorphisms are linear. Over a regular scheme S such as a smooth variety, every projective bundle is of the form P ( E ) {\displaystyle
Projective_bundle
In algebraic geometry, the scheme-theoretic intersection of closed subschemes X, Y of a scheme W is X × W Y {\displaystyle X\times _{W}Y} , the fiber
Scheme-theoretic_intersection
Algorithm to smooth data points
that can be applied to a set of digital data points for the purpose of smoothing the data, that is, to increase the precision of the data without distorting
Savitzky–Golay_filter
Higher-order schemes also exist, but become increasingly complex. Rößler developed many schemes for Ito SDEs, whereas Komori developed schemes for Stratonovich
Runge–Kutta_method_(SDE)
Generalization of algebraic spaces or schemes
for treating these moduli spaces as if their underlying schemes or algebraic spaces are smooth. After Grothendieck developed the general theory of descent
Algebraic_stack
subschemes of some scheme, neither containing the other, have unequal dimensions, then their union is not equidimensional. If a scheme is smooth (for instance
Dimension_of_a_scheme
the fields they stirred up trouble; otherwise, they co-operated in the smooth running of the estate. "Not only did Doll's family have access to slave
Slave-owning_slaves
Historical currencies of China
suppress through heavy taxes, fines, confiscations, and price regulation schemes. During the early Western Han period, founding Emperor Gaozu (r. 202–195
Han_dynasty_coinage
Market and cultural hub in St. Paul, Minnesota
Thai or Lao style Hmong sausage Twin Tropic Cafe: chocolate and blackberry smooth bubble teas; meatball soup (fawm) Xieng Khoung Kitchen: spring rolls Hmongtown
Hmongtown_Marketplace
to X through f have the same étale cohomology, locally. For example, a smooth morphism is universally locally acyclic. Milne, J. S. (1980), Étale cohomology
Locally_acyclic_morphism
off with Mason, asking him out on a date. Theo however corners him and smooth-talks his way up to Corey, then subtly threatens the younger boy that he
List of Teen Wolf (2011 TV series) secondary characters
List_of_Teen_Wolf_(2011_TV_series)_secondary_characters
beings must cooperate in this manner if they are to live together as a smoothly functioning society. — Propaganda (1928) Walter Lippmann, returning from
History_of_propaganda
Concept in applied mathematics
In applied mathematics, the central differencing scheme is a finite difference method that optimizes the approximation for the differential operator in
Central_differencing_scheme
(in Hungarian) Obituary: Anthony Bryceson Anita Carey obituary "Father Of Smooth Jazz" Frank Cody; Longtime Programmer & Broadcast Architecture Co-Founder
Deaths_in_July_2023
resurfacer An ice resurfacer is a truck-like vehicle used to clean and smooth the surface of an ice rink. Frank J. Zamboni of Paramount, California invented
Timeline of United States inventions (1946–1991)
Timeline_of_United_States_inventions_(1946–1991)
Branch of mathematics
noncommutative algebraic geometry is supposed to extend a notion of an algebraic scheme by suitable gluing of spectra of noncommutative rings; depending on how
Noncommutative algebraic geometry
Noncommutative_algebraic_geometry
Entertainment scene in Belgrade, Serbia
Zvezda. Though all the necessary permits were obtained, not everything went smooth. Municipal authorities debated about it, and some described it as a "lair
Nightlife_in_Belgrade
agree to do it. It is the first morning of delivering and things are going smoothly. Wally does get chased by a dog and an old woman asks Ricky to look at
List of The Adventures of Ozzie and Harriet episodes
List_of_The_Adventures_of_Ozzie_and_Harriet_episodes
Structure in algebraic geometry
topology. Assume the category consists of smooth schemes over a qcqs (quasi-compact and quasi-separated) scheme, then the original definition due to NisnevichRemark
Nisnevich_topology
travel, tourism, insurance
SMOOTH SCHEME
SMOOTH SCHEME
SMOOTH SCHEME
SMOOTH SCHEME
SMOOTH SCHEME
SMOOTH SCHEME
SMOOTH SCHEME
SMOOTH SCHEME
SMOOTH SCHEME
travel, tourism, insurance