• Title, Summary, Keyword: higher adeles

Search Result 1, Processing Time 0.019 seconds

SECOND CHERN NUMBERS OF VECTOR BUNDLES AND HIGHER ADELES

  • Osipov, Denis V.
    • Bulletin of the Korean Mathematical Society
    • /
    • v.54 no.5
    • /
    • pp.1699-1718
    • /
    • 2017
  • 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.