Bull. Korean Math. Soc. 2017; 54(5): 1699-1718
Online first article July 3, 2017 Printed September 30, 2017
https://doi.org/10.4134/BKMS.b160687
Copyright © The Korean Mathematical Society.
Denis V. Osipov
Steklov Mathematical Institute of Russsian Academy of Sciences
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 $\Z$-torsor of a locally linearly compact $k$-vector space. Analogs of certain auxiliary results for the case of an arithmetic surface are also discussed.
Keywords: vector bundles, Chern numbers, higher adeles, algebraic and arithmetic surfaces
MSC numbers: 14J60, 14J20
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