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Characteristic classes for algebraic vector bundles with Hermitian metric. II. (English) Zbl 0715.14006
[For part I of this paper see ibid., No.1, 163-203 (1990; Zbl 0715.14018).]
This part II has three sections. In section 5, the case \(X={\mathbb{P}}^ n\) (the projective space) is considered; one computes the arithmetic Chern classes of the canonical rank \(n\) vector bundle on X, which are given by the \(L^ 1\quad forms\) introduced by Levine in his paper on Nevanlinna theory for maps into \({\mathbb{P}}^ n({\mathbb{C}})\) [H. I. Levine, Ann. Math., II. Ser. 71, 529-535 (1960; Zbl 0142.048)]. In section 6, one introduces \(\hat K_ 0(X)\) and one describes it by some exact sequences. In the last section, one gives a new description of the Beilinson regulator on \(K_ 1\)(X) by means of Bott-Chern forms, and one shows that ch is an isomorphism of \(\lambda\)-rings.

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
32H30 Value distribution theory in higher dimensions
57R20 Characteristic classes and numbers in differential topology
14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry
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