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Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)$
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Claire Voisin

Print publication date: 2014

Print ISBN-13: 9780691160504

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691160504.001.0001

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Chow groups of large coniveau complete intersections

Chow groups of large coniveau complete intersections

(p.55) Chapter Four Chow groups of large coniveau complete intersections
Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)

Claire Voisin

Princeton University Press

This chapter first describes how to compute the Hodge coniveau of complete intersections. It then explains a strategy to attack the generalized Hodge conjecture for complete intersections of coniveau 2. The guiding idea is that although the powerful method of the decomposition of the diagonal suggests that computing Chow groups of small dimension is the right way to solve the generalized Hodge conjecture, it might be better to invert the logic and try to compute the geometric coniveau directly. And indeed, this chapter culminates with the proof of the fact that for very general complete intersections, the generalized Hodge conjecture implies the generalized Bloch conjecture.

Keywords:   Hodge coniveau, generalized Hodge conjecture, geometric coniveau, generalized Bloch conjecture, Lefschetz standard conjecture

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