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searching for Closed immersion 22 found (39 total)

Theorem of absolute purity (248 words) [view diff] exact match in snippet view article find links to article

regular scheme X over some base scheme, i:Z→X{\displaystyle i:Z\to X} a closed immersion of a regular scheme of pure codimension r, an integer n that is invertible

Chow's lemma (2,089 words) [view diff] exact match in snippet view article find links to article

by finitely many affine opens Xjk{\displaystyle X_{jk}} each with a closed immersion in to ASjn{\displaystyle \mathbb {A} _{S_{j}}^{n}} since X→S{\displaystyle

Grassmannian (7,870 words) [view diff] exact match in snippet view article find links to article

{\displaystyle T\to \mathbf {Gr} (k,{\mathcal {E}}),} this closed immersion induces a closed immersion P(GT)→P(E)×ST.{\displaystyle \mathbf {P} ({\mathcal {G}}_{T})\to

Formally étale morphism (537 words) [view diff] exact match in snippet view article find links to article

Y-scheme Z, every nilpotent sheaf of ideals J on Z with i : Z0 → Z be the closed immersion determined by J, and every Y-morphism g : Z0 → X, there exists a unique

H topology (1,711 words) [view diff] exact match in snippet view article find links to article

proper morphism of finite presentation, Z→X{\displaystyle Z\to X} is a closed immersion of finite presentation, and X′→X{\displaystyle X'\to X} is an isomorphism

Cotangent complex (4,545 words) [view diff] exact match in snippet view article find links to article

to Kähler differentials is the conormal exact sequence. If f is a closed immersion with ideal sheaf I, then there is an exact sequence I/I2→f∗ΩY/Z→ΩX/Z→0

Six operations (1,002 words) [view diff] exact match in snippet view article find links to article

_{Y}(M,N)\to \operatorname {RHom} _{X}(Lf^{*}M,f^{!}N).} If i is a closed immersion of Z into S with complementary open immersion j, then there is a distinguished

Normal cone (3,148 words) [view diff] exact match in snippet view article find links to article

TX/S{\displaystyle T_{X/S}}. If X↪X′{\displaystyle X\hookrightarrow X'} is a closed immersion and if Y′→Y{\displaystyle Y'\to Y} is a flat morphism such that

Crystalline cohomology (1,905 words) [view diff] exact match in snippet view article find links to article

denoted Cris(X/Wn), has as its objects pairs U→T consisting of a closed immersion of a Zariski open subset U of X into some Wn-scheme T defined by a

Equivariant algebraic K-theory (748 words) [view diff] exact match in snippet view article find links to article

be an equivariant algebraic scheme. Localization theorem — Given a closed immersion Z↪X{\displaystyle Z\hookrightarrow X} of equivariant algebraic schemes

Étale morphism (2,446 words) [view diff] exact match in snippet view article find links to article

i:Z0→Z{\displaystyle i\colon Z_{0}\rightarrow Z} be the canonical closed immersion. Let z{\displaystyle z} denote the closed point of Z0{\displaystyle

Quasi-finite morphism (733 words) [view diff] exact match in snippet view article find links to article

induced map fred between reduced schemes is quasi-finite. If f is a closed immersion, then f is quasi-finite. If X is noetherian and f is an immersion,

Constructible set (topology) (1,636 words) [view diff] exact match in snippet view article

of the following properties: surjective, proper, finite, immersion, closed immersion, open immersion, isomorphism. (Proposition (9.6.1)) Let f:X→S{\displaystyle

Frobenius endomorphism (4,045 words) [view diff] exact match in snippet view article find links to article

X → S is an open immersion, then it is the identity. If X → S is a closed immersion determined by an ideal sheaf I of OS, then X(p) is determined by the

Equivariant sheaf (1,438 words) [view diff] exact match in snippet view article find links to article

Also, if L is very ample and linearized, then there is a G-linear closed immersion from X to PN{\displaystyle \mathbf {P} ^{N}} such that OPN(1){\displaystyle

Cone (algebraic geometry) (1,251 words) [view diff] exact match in snippet view article

locally generates R as R0{\displaystyle R_{0}}-algebra. Then there is a closed immersion SpecX⁡R↪C(R1){\displaystyle \operatorname {Spec} _{X}R\hookrightarrow

Grothendieck topology (4,500 words) [view diff] exact match in snippet view article find links to article

structure sheaves, which this map does not do. In fact, this map is a closed immersion. The étale topology is finer than the Zariski topology. It was the

Flat morphism (3,471 words) [view diff] exact match in snippet view article find links to article

isomorphism. A monomorphism. An open immersion. A quasi-compact immersion. A closed immersion. Affine. Quasi-affine. Finite. Quasi-finite. Integral. It is possible

Jouanolou's trick (984 words) [view diff] exact match in snippet view article find links to article

case. If X is projective over an affine scheme S, then it admits a closed immersion into some projective space PSr{\displaystyle \mathbf {P} _{S}^{r}}

Coherent sheaf cohomology (4,452 words) [view diff] exact match in snippet view article find links to article

can be used to define a map from X to projective space, perhaps a closed immersion. This approach is essential for classifying algebraic varieties. The

Torsor (algebraic geometry) (2,535 words) [view diff] exact match in snippet view article

Y\times ^{G}H}. If the morpshims b:G→H{\displaystyle b:G\to H} is a closed immersion then Y{\displaystyle Y} is said to be a sub-torsor of T{\displaystyle

Residual intersection (3,116 words) [view diff] exact match in snippet view article find links to article

{g}}:{\widetilde {X}}\to X} the restriction of f. Assume f can be written as a closed immersion followed by a smooth morphism (for example, Y is quasi-projective)