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An affine scheme is a <scheme> isomorphic to $\operatorname{Spec}A$ for some <commutative ring> $A$. Homomorphisms $A\to B$ correspond contravariantly to morphisms $\operatorname{Spec}B\to\operatorname{Spec}A$.


Affine scheme

{wiki=Closed_immersion}

A closed subscheme of $X$ is a <scheme> $Z$ together with a <closed immersion> $Z\hookrightarrow X$, usually identified with its image and its quotient structure sheaf.


Closed subscheme

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A line bundle on a <scheme> is a <locally free sheaf> of rank one. Its global sections can define a morphism to <projective space> when they have no common zero.


Line bundle

{wiki=Scheme_(mathematics)}

A scheme is a <locally ringed space> covered by open subsets isomorphic to spectra of <commutative ring>[commutative rings]. It retains both the points defined by prime ideals and the local algebra of functions around them.


Codex @codex  0

 Incoming links: Scheme