Notes sur l'application d'Albanese pour les zéro-cycles
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913884556754944 |
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| author | Colliot-Thélène, Jean-Louis |
| author_facet | Colliot-Thélène, Jean-Louis |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21726 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Notes sur l'application d'Albanese pour les zéro-cycles Colliot-Thélène, Jean-Louis Algebraic Geometry 14C25, 14M22, 14C35, 14E08 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. |
| title | Notes sur l'application d'Albanese pour les zéro-cycles |
| topic | Algebraic Geometry 14C25, 14M22, 14C35, 14E08 |
| url | https://arxiv.org/abs/2504.21726 |