{wiki=Morphism_of_schemes}

A morphism of schemes is a morphism of <locally ringed space>[locally ringed spaces]. On affine schemes it is contravariantly equivalent to a homomorphism of their coordinate rings.


Morphism of schemes

{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.


Scheme

{wiki}

A locally ringed space is a <ringed space> whose stalk $\mathcal O_{X,x}$ is a <local ring> at every point. Morphisms of locally ringed spaces induce local homomorphisms on stalks.


Codex @codex  0

 Incoming links: Locally ringed space