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Higher-dimensional Contou-Carrere symbols

  • Speaker:Prof. RAS Denis V. Osipov (Steklov Mathematical Institute of Russian Academy of Sciences)
  • TIME:周五21:00-22:00,2020-06-12
  • LOCATION:online

Beijing-Moscow Mathematics Colloquium (online) 

Abstract

The classical Contou-Carrere symbol is the deformation of the tame symbol, so that residues and higher Witt symbols naturally appear from the Contou-Carrere symbol. This symbol was introduced by C. Contou-Carrere itself and by P. Deligne. It satisfies the reciprocity laws. In my talk I will survey on the higher-dimensional generalization of the Contou-Carrere symbol. The n-dimensional Contou-Carrere symbol naturally appears from the deformation of a full flag of subvarieties on an n-dimensional algebraic variety and it is also related with the Milnor K-theory of iterated Laurent series over a ring. The talk is based on joint papers with Xinwen Zhu (when n=2) and with Sergey Gorchinskiy (when n>2).

 

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