Zero-cycles in families of rationally connected varieties

• Morten Lüders ^[1]
  1. [1] Heidelberg University

     Heidelberg University

     Stadtkreis Heidelberg, Alemania

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 4, 2024, págs. 1-43
• Idioma: inglés
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• Resumen

  • 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).