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...

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...

} 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...

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

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...

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...

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...

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

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...

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...

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

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...

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...

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...

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

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

mathematics, in particular 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...

finiteness theorems. Ahlfors finiteness theorem Finiteness theorem for a proper morphism Compactness theorem, in mathematical logic This disambiguation page...

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...

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

sheaf F. Here j is any open immersion of X into a scheme Y with a proper morphism g to S (with f = gj), and as before the definition does not depend...

contiguous land empire in history. His grandson Kublai Khan conquered China proper and established the Yuan dynasty. After the collapse of the Yuan, the Mongols...

. {\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...

every C-morphism f : FY → X, there is a unique D-morphism ΦY, X(f) = g : Y → GX such that the diagrams below commute, and for every D-morphism g : Y →...

{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...

for classical genetics by John Maynard Smith (1998). The shorter term morphism was preferred by the evolutionary biologist Julian Huxley (1955). Various...

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

is different from n. This overloaded word is also non-jargon for a proper morphism. regular A function is called regular if it satisfies satisfactory...