2026-04-17T01:41:52Zhttps://recercat.cat/oai/request

oai:recercat.cat:2072/4524232024-06-06T09:43:40Zcom_2072_98col_2072_378195

00925njm 22002777a 4500 dc Burgos Gil, José Ignacio author Centre de Recerca Matemàtica author 2007 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 this 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. Homologia, Teoria d' Grups aritmètics Semipurity of tempered Deligne cohomology