Semipurity of tempered Deligne cohomology

Details Semipurity of tempered Deligne cohomology Semipurity of tempered Deligne cohomology

2010-11-16

arxiv.org/abs/1011.3714v1

Burgos Gil, J. I., Semipurity of tempered Deligne cohomology. Collect. Math. 59 (2008), no. 1, 79-102

Mathematics

Algebraic Geometry

Scientific paper

10.1007/BF03191183

In this paper we define the formal and tempered Deligne cohomology groups, that are obtained by applying the Deligne complex functor to the complexes of formal differential forms and tempered currents respectively. We then prove the existence of a duality between them, a vanishing theorem for the former and a semipurity property for the latter. The motivation of these results comes from the study of covariant arithmetic Chow groups. The semi-purity property of tempered Deligne cohomology implies, in particular, that several definitions of covariant arithmetic Chow groups agree for projective arithmetic varieties.

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