On the Deligne--Beilinson cohomology sheaves

Details On the Deligne--Beilinson cohomology sheaves On the Deligne--Beilinson cohomology sheaves

1994-12-07

arxiv.org/abs/alg-geom/9412006v1

Mathematics

Algebraic Geometry

12 pages, LaTeX 2.09

Scientific paper

We are showing that the Deligne--Beilinson cohomology sheaves ${\cal H}^{q+1}({\bf Z}(q)_{\cal D})$ 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 $p_g=0$.

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