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Title: Semi-purity of tempered Deligne cohomology
Author: Burgos Gil, José I.
Keywords: Geometria algebraica
Algebraic geometry
Issue Date: 2008
Publisher: Universitat de Barcelona
Abstract: 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.
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It is part of: Collectanea Mathematica, 2008, vol. 59, num. 1, p. 79-102
ISSN: 0010-0757
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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