In number theory, a Parshin chain is a higher-dimensional analogue of a place of an algebraic number field. They were introduced by in order to define an analogue of the idele class group for 2-dimensional schemes.
A Parshin chain of dimension s on a scheme is a finite sequence of points p<sub>0</sub>, p<sub>1</sub>, ..., p<sub>s</sub> such that p<sub>i</sub> has dimension i and each point is contained in the closure of the next one.