In mathematics, the Contou-Carrère symbol, named after Carlos Contou-Carrère, is a Steinberg symbol defined on pairs of invertible elements of the ring of Laurent power series over an Artinian ring , taking values in the group of units of .
Definition
If is an Artinian local ring, then any invertible formal Laurent series with coefficients in can be written uniquely as
where is an integer, is a unit, and the elements are in , and are in for .
The Contou-Carrère symbol of and is defined to be
References