The rank of étale cohomology of varieties over -adic or number fields
K-théorie des anneaux d'entiers de corps de nombres et cohomologie étale.
A vanishing theorem on arithmetic surfaces.
Groupes de Chow et K-théorie de variétés sur un corps fini.
Successive minima on arithmetic varieties
Erratum : “The rank of étale cohomology of varieties over -adic or number fields”
Intersection theory using Adams operations.
Descent, motives and K-theory.
On the arithmetic Chern character
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”...
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