Аннотация:
The talk is based on a joint work with Sergey Gorchinskiy. The n-dimensional Contou-Carrère symbol is a universal deformation of the n-dimensional tame symbol such that it satisfies the Steinberg property from algebraic K-theory and it is possible to obtain the n-dimensional residue from this symbol. I will give various equivalent definitions of the n-dimensional Contou-Carrère symbol: 1) by an explicit "analytic’’ formula over Q-algebras, 2) by means of the action of the group of continuous automorphisms of iterated Laurent series over a ring, 3) by means of algebraic K-theory. I will explain also the universal property for the n-dimensional Contou-Carrère symbol, the proof of which is based on the statement that the tangent map to the map given by the n-dimensional Contou-Carrère symbol is the n-dimensional residue.