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{{short description|Theorem in algebraic topology about the complex K-theory spectrum}} ...uced by [[Victor Snaith]], identifies the [[complex K-theory]] [[spectrum (topology)|spectrum]] with the [[localization of a spectrum|localization]] of the sus ...

{{short description|Offers a substitute for the absence of excision in homotopy theory}} ...em''' offers a substitute for the absence of [[Excision theorem|excision]] in [[homotopy theory]]. More precisely, let <math>(X; A, B)</math> be an [[exc ...

{{Short description|Two theorems needed for Quillen's Q-construction in algebraic K-theory}} .... The two theorems play central roles in Quillen's [[Q-construction]] in [[algebraic K-theory]] and are named after [[Daniel Quillen]]. ...

{{short description|Result in algebraic K-theory relating Chow groups to cohomology}} ...matics)|field]] is isomorphic to the cohomology of ''X'' with coefficients in the K-theory of the structure sheaf <math>\mathcal{O}_X</math>; that is, ...

{{DISPLAYTITLE:Basic theorems in algebraic ''K''-theory}} {{short description|Four mathematical theorems}} ...

{{DISPLAYTITLE:Fundamental theorem of algebraic ''K''-theory}} In [[algebra]], the '''fundamental theorem of [[algebraic K-theory|algebraic ''K''-theory]]''' describes the effects of [[change of rings|changing the r ...

...of ''X'' there is a fundamental system of neighborhoods (in the classical topology) of ''x'' whose intersection with ''Y'' is connected. ...unibranch and geometrically unibranch points are used in some theorems in algebraic geometry. For example, there is the following result: ...

...id are the purely algebraic analogue of this construction, giving a purely algebraic description of quasi-coherent sheaves on a stack: this is one of the first == Structure theorems == ...

...matics)|knot]]s or [[link (knot theory)|link]]s. The conditions are stated in terms of the [[group (mathematics)|group]] structures on braids. ...ates that every [[knot (mathematics)|knot]] or [[link (knot theory)|link]] in three-dimensional Euclidean space is the closure of a [[braid (mathematics) ...

The '''Mackey–Arens theorem''' is an important theorem in [[functional analysis]] that characterizes those [[locally convex]] [[Topol {{Main|Polar topology|Mackey topology}} ...

In mathematics, the '''twisted Poincaré duality''' is a theorem removing the r ...theorem with real coefficients features [[de Rham cohomology]] with values in the '''orientation bundle'''. This is the '''[[flat vector bundle|flat]]''' ...

In [[algebraic topology]], '''Hilton's theorem''', proved by {{harvs|txt|first=Peter|last=Hilton|au ...year=1972}} showed more generally that the loop space of the [[Suspension (topology)|suspension]] of a wedge of spaces can be written as an infinite product of ...

...braic scheme ''X'' with [[linear algebraic group action|action of a linear algebraic group]] ''G'', via Quillen's [[Q-construction]]; thus, by definition, ...2–1995)].</ref> Specifically, he proved equivariant analogs of fundamental theorems such as the localization theorem. ...

...y simple [[Brown–Peterson cohomology|BP-homology]], and are useful objects in [[stable homotopy theory]]. ...ihQC&q=Larry+Smith+algebraic+topology&pg=PA341|title=Handbook of Algebraic Topology|last=James|first=I. M.|date=1995-07-18|publisher=Elsevier|isbn=978008053298 ...

In [[algebraic geometry]], the '''Atiyah–Bott formula''' says<ref>{{harvnb|Gaitsgory|Lurie [[Category:Theorems in algebraic geometry]] ...

...motopy group|homotopy groups]] of a [[ring spectrum]] to be [[nilpotent]], in terms of the [[complex cobordism]] spectrum <math>\mathrm{MU}</math>. More ...ation | last=Ravenel | first=Douglas C. | title=Nilpotence and periodicity in stable homotopy theory | url=https://books.google.com/books?isbn=069102572X ...

...ecause it allows one to construct analogues of [[algebraic number field]]s in the p-adic context. One of the useful structure theorems for vector spaces over locally compact fields is that the finite dimensiona ...

{{Short description|Mathematical result about equivariant K-theory in homotopy theory}} ...''' is a [[theorem]] in [[mathematics]] about [[equivariant]] [[K-theory]] in [[homotopy theory]]. Let ''G'' be a [[compact group|compact]] [[Lie group]] ...

...s function|continuous]] at [[zero]] in the ''Sazonov topology'' and such a topology is called ''sufficient''. The theorem is named after the two [[Russia|Russi ...t |last=Schwartz |publisher=Tata Institute of Fundamental Research Studies in Mathematics |title=Radon measures on arbitrary topological spaces and cylin ...

In mathematics, the first '''Blakers–Massey theorem''', named after [[Albert B ...| last=Hatcher | first=Allen | authorlink=Allen Hatcher| title= Algebraic Topology, Theorem 4.23 }}</ref> gave vanishing conditions for certain [[excisive tri ...