= Solution
A <morphism of schemes> is a <morphism of locally ringed spaces>. Thus it consists of a continuous map $f:|X|\to|Y|$ and a homomorphism of <sheaves of rings>
$$
f^\#: \mathcal O_Y\longrightarrow f_*\mathcal O_X
$$
such that, for every $x\in X$, the induced map on <stalks>
$$
f_x^\#: \mathcal O_{Y,f(x)}\longrightarrow\mathcal O_{X,x}
$$
is a <local homomorphism>: it carries the maximal ideal of the source into the maximal ideal of the target. Equivalently, the inverse image of the target maximal ideal is the source maximal ideal. \b[The locality condition on every <stalk> distinguishes a <morphism of schemes> from a general morphism of ringed spaces.]
Back to article page
