nLab
k-ring of functions on a k-functor

Definition

Recall that the affine line O k=M k(k[t],) is an affine k-scheme. Let M k denote the category of k-rings.

A function on a k-scheme X is defined to be an object fO(X):=coPsh(M k)(X,O k). O(X) is a k-ring by component-wise addition and -multiplication.

Proposition

There is an adjoint equivalence

(SpO):Sch affORing k(Sp\dashv O):Sch_{aff}\stackrel{O}{\to}Ring_k

of the categories of affine k-schemes and k-rings.

ringed space

Revised on June 5, 2012 17:15:43 by Stephan Alexander Spahn (178.195.231.138)