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searching for Noetherian scheme 11 found (47 total)

Cartan's theorems A and B (409 words) [view diff] exact match in snippet view article find links to article

sheaves F on a complex manifold X (resp. quasi-coherent sheaves F on a noetherian scheme X), then X is Stein (resp. affine); see (Serre 1956) (resp. (Serre

Gorenstein scheme (679 words) [view diff] exact match in snippet view article find links to article

In algebraic geometry, a Gorenstein scheme is a locally Noetherian scheme whose local rings are all Gorenstein. The canonical line bundle is defined for

Resolution of singularities (5,480 words) [view diff] exact match in snippet view article find links to article

set. Lipman (1978) showed that a surface Y (a 2-dimensional reduced Noetherian scheme) has a desingularization if and only if its normalization is finite

Weibel's conjecture (498 words) [view diff] exact match in snippet view article find links to article

(2014), and Morrow (2016). Weibel's conjecture asserts that for a Noetherian scheme X of finite Krull dimension d, the K-groups vanish in degrees < −d:

Hypercovering (575 words) [view diff] exact match in snippet view article find links to article

colimit of the cochain cohomologies over all hypercovers. For a locally Noetherian scheme X {\displaystyle X} , the category H R ( X ) {\displaystyle HR(X)}

Nisnevich topology (1,767 words) [view diff] exact match in snippet view article find links to article

topology is the existence of a descent spectral sequence. Let X be a Noetherian scheme of finite Krull dimension, and let Gn(X) be the Quillen K-groups of

Algebraic cycle (1,472 words) [view diff] exact match in snippet view article find links to article

: X → S {\displaystyle \phi \colon X\to S} , where S is a regular Noetherian scheme. An r-cycle is a formal sum of closed integral subschemes of X whose

Group scheme (2,860 words) [view diff] exact match in snippet view article find links to article

example, any finite group scheme is complete. A group scheme G over a noetherian scheme S is finite and flat if and only if OG is a locally free OS-module

Jouanolou's trick (1,001 words) [view diff] exact match in snippet view article find links to article

ample family of line bundles, as does any separated locally factorial Noetherian scheme. Thomason's proof abstracts the key features of Jouanolou's. By hypothesis

Cohen–Macaulay ring (3,123 words) [view diff] exact match in snippet view article find links to article

See also Generalized Cohen–Macaulay ring. We say that a locally Noetherian scheme X {\displaystyle X} is Cohen–Macaulay if at each point x ∈ X {\displaystyle

Projective variety (7,499 words) [view diff] exact match in snippet view article find links to article

As a corollary to 1. above, if f is a projective morphism from a noetherian scheme to a noetherian ring, then the higher direct image R p f ∗ F {\displaystyle