Équivalence rationnelle sur les hypersurfaces cubiques de mauvaise réduction |
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Authors: | David A Madore |
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Institution: | ENS, Paris, France |
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Abstract: | This article consists of two independent, but related, parts. The first one proves the vanishing of the Chow group of classes of zero-cycles of degree zero modulo rational equivalence for a cubic hypersurface of dimension ?10 on a p-adic or C2 field (and, in fact, the R-triviality of such a hypersurface). This is done without the assumption of good reduction (or even smoothness). The second part goes in the other direction and gives an explicit example of a smooth cubic hypersurface of dimension 3 (necessarily of bad reduction) on a field such as C((ν,t)) (or C((ν))((t))) whose Chow group of classes of zero-cycles of degree zero modulo rational equivalence does not vanish. |
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