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SECOND CHERN NUMBERS OF VECTOR BUNDLES AND HIGHER ADELES

  • Osipov, Denis V. (Steklov Mathematical Institute of Russsian Academy of Sciences)
  • Received : 2016.08.17
  • Accepted : 2016.12.02
  • Published : 2017.09.30

Abstract

We give a construction of the second Chern number of a vector bundle over a smooth projective surface by means of adelic transition matrices for the vector bundle. The construction does not use an algebraic K-theory and depends on the canonical ${\mathbb{Z}}-torsor$ of a locally linearly compact k-vector space. Analogs of certain auxiliary results for the case of an arithmetic surface are also discussed.

Acknowledgement

Supported by : Russian Science Foundation

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