flat morphism
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Flat morphism — In mathematics, in particular in the theory of schemes in algebraic geometry, a flat morphism f from a scheme X to a scheme Y is a morphism such that the induced map on every stalk is a flat map of rings, i.e., : fP : OY,f(P) → OX,P is a flat map … Wikipedia
Flat — or flats may refer to:* Flatness * Flat (music), a symbol which denotes a lower pitch (music|flat) * Flat, an apartment within a residential building * Flat (geometry), the generalization of lines and planes in an n dimensional Euclidean space *… … Wikipedia
Flat module — In abstract algebra, a flat module over a ring R is an R module M such that taking the tensor product over R with M preserves exact sequences.Vector spaces over a field are flat modules. Free modules, or more generally projective modules, are… … Wikipedia
Flat topology — In mathematics, the flat topology is a Grothendieck topology used in algebraic geometry. It is used to define the theory of flat cohomology; it also has played a fundamental role in the theory of descent (faithfully flat descent). [… … Wikipedia
Étale morphism — In algebraic geometry, a field of mathematics, an étale morphism (pronunciation IPA|) is an algebraic analogue of the notion of a local isomorphism in the complex analytic topology. They satisfy the hypotheses of the implicit function theorem,… … Wikipedia
List of mathematics articles (F) — NOTOC F F₄ F algebra F coalgebra F distribution F divergence Fσ set F space F test F theory F. and M. Riesz theorem F1 Score Faà di Bruno s formula Face (geometry) Face configuration Face diagonal Facet (mathematics) Facetting… … Wikipedia
Hilbert's Nullstellensatz — (German: theorem of zeros, or more literally, zero locus theorem – see Satz) is a theorem which establishes a fundamental relationship between geometry and algebra. This relationship is the basis of algebraic geometry, an important branch of… … Wikipedia
Flatness — The intuitive idea of flatness is important in several fields.Flatness in mathematicsThe flatness of a surface is the degree to which it approximates a mathematical plane. The term is generalized for higher dimensional manifolds to describe the… … Wikipedia
List of algebraic geometry topics — This is a list of algebraic geometry topics, by Wikipedia page. Contents 1 Classical topics in projective geometry 2 Algebraic curves 3 Algebraic surfaces 4 … Wikipedia
Séminaire Nicolas Bourbaki (1950–1959) — Continuation of the Séminaire Nicolas Bourbaki programme, for the 1950s. 1950/51 series *33 Armand Borel, Sous groupes compacts maximaux des groupes de Lie, d après Cartan, Iwasawa et Mostow (maximal compact subgroups) *34 Henri Cartan, Espaces… … Wikipedia
Localization of a module — In mathematics, the localization of a module is a construction to introduce denominators in a module for a ring. More precisely, it is a systematic way to construct a new module S −1 M out of a given module M containing fractions… … Wikipedia
