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arXiv · 2504.21726

Notes sur l'application d'Albanese pour les z\'ero-cycles

Jean-Louis Colliot-Thélène
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Abstract

For a smooth projective variety X over an arbitrary field k, we discuss the surjectivity of the Albanese map from the Chow group of zero-cycles of degree zero on X to the group of rational points of the Albanese variety of X. Over arithmetic fields, we use Severi-Brauer fibrations to produce examples where the map is not surjective. For varieties X over the complex field, we discuss the question after extension of the complex field to function fields of varieties. This is related to C. Voisin's notion of universal zero-cycle and to rationality questions for rationally connected threefolds.

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Jean-Louis Colliot-Thélène. 2025-04-30. Notes sur l'application d'Albanese pour les z\'ero-cycles. https://arxiv.org/abs/2504.21726

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