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searching for Noetherian scheme 11 found (47 total)

alternate case: noetherian scheme

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