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2008

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/16924

Semi-purity of tempered Deligne cohomology

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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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Geometria algebraica

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Algebraic geometry

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BURGOS GIL, José I. Semi-purity of tempered Deligne cohomology. Collectanea Mathematica. 2008. Vol. 59, num. 1, pags. 79-102. ISSN 0010-0757. [consulted: 17 of June of 2026]. Available at: https://hdl.handle.net/2445/16924

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