Parshin chain

In number theory, a Parshin chain is a higher-dimensional analogue of a place of an algebraic number field. They were introduced by Parshin (1978) 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 p₀, p₁, ..., p_s such that p_i has dimension i and each point is contained in the closure of the next one.