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On the cycle class map for zero-cycles over local fields

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Formale Metadaten

Titel On the cycle class map for zero-cycles over local fields
Serientitel Conférences Paris Pékin Tokyo
Teil 10
Anzahl der Teile 15
Autor Wittenberg, Olivier
Lizenz CC-Namensnennung 3.0 Unported:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/20490
Herausgeber Institut des Hautes Études Scientifiques (IHÉS)
Erscheinungsjahr 2014
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Mathematik
Abstract Séminaire de Géométrie Arithmétique Paris-Pékin-Tokyo avec Olivier Wittenberg (ENS et CNRS) The Chow group of zero-cycles of a smooth and projective variety defined over a field k is an invariant of an arithmetic and geometric nature which is well understood only when k is a finite field (by higher-dimensional class field theory). In this talk, we will discuss the case of local and strictly local fields. We prove in particular the injectivity of the cycle class map to integral l-adic cohomology for a large class of surfaces with positive geometric genus over p-adic fields. The same statement holds for semistable K3 surfaces over C((t)), but does not hold in general for surfaces over C((t)) or over the maximal unramified extension of a p-adic field. This is a joint work with Hélène Esnault.

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