X → Y be a morphism of schemes. The composition of two proper morphisms is proper. Any base change of a proper morphism f: X → Y is proper. That is, if...

is called proper if inverse images of compact subsets are compact. In algebraic geometry, the analogous concept is called a proper morphism. There are...

compact subsets are compact Proper morphism, in algebraic geometry, an analogue of a proper map for algebraic varieties Proper transfer function, a transfer...

a proper morphism. Then one can write f = g ∘ f ′ {\displaystyle f=g\circ f'} where g : S ′ → S {\displaystyle g\colon S'\to S} is a finite morphism and...

a scheme will be a scheme over some fixed base scheme S and a morphism an S-morphism. Contents:  !$@ A B C D E F G H I J K L M N O P Q R S T U V W XYZ...

of positive dimension is not complete. The morphism taking a complete variety to a point is a proper morphism, in the sense of scheme theory. An intuitive...

algebraic geometry. It roughly says that a proper morphism is fairly close to being a projective morphism. More precisely, a version of it states the...

of Jean-Pierre Serre was extended to a proper morphism; Serre duality was recovered as the case of the morphism of a non-singular projective variety (or...

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...

} Proper base change theorems for quasi-coherent sheaves apply in the following situation: f : X → S {\displaystyle f:X\to S} is a proper morphism between...

morphism has the property that L {\displaystyle L} is the pullback f ∗ O ( 1 ) {\displaystyle f^{*}{\mathcal {O}}(1)} . Conversely, for any morphism f...

respectively. The morphism f is determined by its values on the letters of B and conversely any map from B to M extends to a morphism. A morphism is non-erasing...

separated and finite type morphism to a Noetherian scheme S can be factored into an open immersion followed by a proper morphism. Nagata's original proof...

a proper morphism were proved by Grothendieck (for locally Noetherian schemes) and by Grauert (for complex analytic spaces). Namely, for a proper morphism...

{Spec} (A\otimes _{B}C).} The morphism X ×Y Z → Z is called the base change or pullback of the morphism X → Y via the morphism Z → Y. In some cases, the fiber...

. {\displaystyle H^{2\dim(X)-2d}(X,\mathbb {Q} ).} Now consider a proper morphism f : X → Y {\displaystyle f\colon X\to Y} between smooth quasi-projective...

Morph the Cat is the third studio album by American singer-songwriter Donald Fagen. Released on March 7, 2006, to generally positive reviews from critics...

unramified at x. Finite morphisms are quasi-finite. A quasi-finite proper morphism locally of finite presentation is finite. Indeed, a morphism is finite if and...

G-maps. The composition of two morphisms is again a morphism. If a morphism f is bijective, then its inverse is also a morphism. In this case f is called an...

algébrique Fiber product of schemes Flat morphism Smooth scheme Finite morphism Quasi-finite morphism Proper morphism Semistable elliptic curve Grothendieck's...

sections. Let f : X → Y {\displaystyle f:X\to Y} be a morphism of ringed spaces (for example, a morphism of schemes). If F {\displaystyle {\mathcal {F}}} is...

and the Hom functor on modules. Flat morphism, Smooth morphism, Proper morphism, Finite morphism, Étale morphism Stable curve Birational geometry Étale...

finite surjective morphism f: X → Y, X and Y have the same dimension. By Deligne, a morphism of schemes is finite if and only if it is proper and quasi-finite...

Parafactorial local ring Projective tensor product Proper morphism – in algebraic geometry, an analogue of a proper map for algebraic varietiesPages displaying...

object x, there exists a morphism 1x : x → x (some authors write idx) called the identity morphism for x, such that every morphism f : a → x satisfies 1x...

a universal morphism from • to U. The functor which sends • to I is left adjoint to U. A terminal object T in C is a universal morphism from U to •....

conditions are equivalent. There exists a morphism t : B → A such that t ∘ f is the identity on A. There exists a morphism u: C → B such that g ∘ u is the identity...

morphism of schemes generalizes a morphism of algebraic varieties just as a scheme generalizes an algebraic variety. It is, by definition, a morphism...

X {\displaystyle X} . A morphism φ : F → G {\displaystyle \varphi :{\mathcal {F}}\to {\mathcal {G}}} consists of a morphism φ U : F ( U ) → G ( U ) {\displaystyle...

associated to the proper morphism Z → X {\displaystyle Z\to X} , and the second homomorphism is pullback with respect to the flat morphism X − Z → X {\displaystyle...