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Semi-purity of tempered Deligne cohomology
Burgos Gil, José I.
Universitat de Barcelona
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 semipurity property of tempered Deligne cohomology implies, in particular, that several definitions of covariant arithmetic Chow groups agree for projective arithmetic varieties.
Geometria algebraica
Algebraic geometry
(c) Burgos, 2008
Universitat de Barcelona

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