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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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Integral coefficients

Integral coefficients

Chapter:
(p.123) Chapter Six Integral coefficients
Source:
Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)
Author(s):

Claire Voisin

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691160504.003.0006

This chapter turns to a number of birational invariants that can be defined using Z-coefficients. It is devoted in part to the study of the groups Z²ⁱ(X) measuring the failure of the Hodge conjecture with integral coefficients. Some vanishing and nonvanishing results are presented, together with a comparison of the group Z⁴(X) with the so-called unramified cohomology of X with torsion coefficients. This chapter also considers various forms of the existence of an integral cohomological decomposition of the diagonal of a threefold X with trivial CH₀ group. It shows that an affirmative answer to this question is equivalent to the vanishing of numerous birational invariants of X.

Keywords:   integral coefficients, birational invariants, Z-coefficients, unramified cohomology, torsion coefficients, integral cohomological decomposition

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