Zero-cycles in families of rationally connected varieties
We study zero-cycles in families of rationally connected varieties. We show that for a smooth projective scheme over a henselian discrete valuation ring the restriction of relative zero cycles to the special fiber induces an isomorphism on Chow groups if the special fiber is separably rationally con...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
9 July 2024
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| In: |
Selecta mathematica
Year: 2024, Volume: 30, Issue: 4, Pages: 1-43 |
| ISSN: | 1420-9020 |
| DOI: | 10.1007/s00029-024-00963-1 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1007/s00029-024-00963-1
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| Author Notes: | Morten Lüders |
| Summary: | We study zero-cycles in families of rationally connected varieties. We show that for a smooth projective scheme over a henselian discrete valuation ring the restriction of relative zero cycles to the special fiber induces an isomorphism on Chow groups if the special fiber is separably rationally connected. We further extend this result to certain higher Chow groups and develop conjectures in the non-smooth case. Our main results generalise a result of Kollár (Publ. Res. Inst. Math. Sci. 40(3):689-708, 2004). |
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| Item Description: | Gesehen am 12.12.2024 |
| Physical Description: | Online Resource |
| ISSN: | 1420-9020 |
| DOI: | 10.1007/s00029-024-00963-1 |