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, ..., ps such that pi has dimension i and each point is contained in the closure of the next one.
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