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On the arithmetic Chern character. (English. French summary) Zbl 1326.14064
Summary: We consider a short sequence of hermitian vector bundles on some arithmetic variety. Assuming that this sequence is exact on the generic fiber we prove that the alternated sum of the arithmetic Chern characters of these bundles is the sum of two terms, namely the secondary Bott Chern class of the sequence and its Chern character with support on the finite fibers.
Next, we compute these classes in the situation encountered by the second author when proving a “Kodaira vanishing theorem” for arithmetic surfaces.
MSC:
14G40 Arithmetic varieties and schemes; Arakelov theory; heights
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
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