On the Deligne--Beilinson cohomology sheaves

Abstract

We are showing that the Deligne--Beilinson cohomology sheaves ${\mathcal{H}}^{q+1}(\mathbf{Z}(q{)}_{\mathcal{D}})$ are torsion free by assuming Kato's conjectures hold true for function fields. This result is `effective' for $q=2$; in this case, by dealing with `arithmetic properties' of the presheaves of mixed Hodge structures defined by singular cohomology, we are able to give a cohomological characterization of the Albanese kernel for surfaces with $p_g=0$.

arXiv comment12 pages, LaTeX 2.09

References in corpus (1)

• Cohomologie non ramifiée et conjecture de Hodge entière

Cited by in corpus (1)

• Cohomologie non ramifiée et conjecture de Hodge entière