• 대한수학회보
• /
• 제54권5호
• /
• 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.