Given an integral scheme $X$, let $K(X)=\mathrm{Frac}(R)$ be its function field, where $\mathrm{Spec}(R)$ is some non-empty open affine subscheme of $X$. Take the maximal ideal $P$ of some DVR of $K(X)$ (i.e. a place $P$). How can one associate a closed point of $X$? Does it exist a bijection between closed points of $X$ and places of $K(X)$?
places of function field and closed point of a scheme
1
$\begingroup$
algebraic-geometry
ideals
schemes
function-fields
-
0I$n$ fact, any valuation determines uniquely a point of the scheme (not a closed point, though) as its center if and only if the scheme is separated. – 2012-12-14