The Generalized Hodge and Bloch Conjectures are Equivalent for General Complete Intersections, II
By Claire Voisin. 2011
77 citations recorded by the source corpus.
We prove an unconditional (but slightly weakened) version of the main result of (13), which was, starting from dimension 4, conditional to the Lefschetz standard conjecture. Let X be a variety with trivial Chow groups, (i.e. the cycle class map to cohomology is injective on CH(X)Q). We prove that if the cohomology of a general hypersurface Y in X is "parameterized by cycles of dimension c", then the Chow groups CHi(Y )Q are trivial for i ≤ c − 1.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/464527034328ffdd41d77e7a71166d00443bbb32
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
In Geometry and Topology
- Claire Voisin
- G. Farkas
- M. Aprodu
- Stefan Schreieder
- Charles Vial
- D. Huybrechts
- Brendan Hassett
- M. Shen
Citations in the corpus
- Chow Rings, Decomposition of the Diagonal, and the Topology of Families (2014, background): “3 is crucial for our proof of the equivalence of the generalized Bloch and Hodge conjectures for very general complete intersections in varieties with trivial Chow groups (see [114] and Section 4.”
- BLOCH'S CONJECTURE FOR CATANESE AND BARLOW SURFACES (2012, methodology): “This lemma is one of the key observations in [27].”