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Многомерные вычеты и тропическая геометрия
14 июня 2021 г. 15:30–16:30, Секция I, г. Сочи
 


Higher-dimensional Contou-Carrère symbol, II

D. V. Osipovabc

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b National Research University "Higher School of Economics", Moscow
c National University of Science and Technology «MISIS», Moscow
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D. V. Osipov



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 ${\mathbb Q}$-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.

Язык доклада: английский

Website: https://us02web.zoom.us/j/2162766238?pwd=TTBraGwvQ3Z3dWVpK3RCSFNMcWNNZz09

* ID: 216 276 6238, password: residue
 
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