The note claims a description of A1 for cubic fourfolds in terms of zero-cycles on surfaces and a resulting non-rationality criterion, but the main theorem is unstated and the proof is internally inconsistent.
(French) [Quartic hypersurfaces in dimension 3: stable non-rationality] , Ann
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A remark on algebraic cycles on cubic fourfolds
The note claims a description of A1 for cubic fourfolds in terms of zero-cycles on surfaces and a resulting non-rationality criterion, but the main theorem is unstated and the proof is internally inconsistent.