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Regular version of the site

Article

Second Chern numbers of vector bundles and higher adeles

Bulletin of the Korean Mathematical Society. 2017. Vol. 54. No. 5. P. 1699-1718.

We gave 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.