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arXiv · 1706.07354

Second Chern numbers of vector bundles and higher adeles

D. V. Osipov
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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.

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D. V. Osipov. 2017-06-22. Second Chern numbers of vector bundles and higher adeles. https://doi.org/10.4134/bkms.b160687

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