Torsion in the Lichtenbaum Chow group of arithmetic schemes

We give an example of a smooth arithmetic scheme $\mathfrak{X} \to B$ over the spectrum of a Dedekind domain and primes $p$ with the property that the $p$-primary torsion subgroup of the Lichtenbaum Chow group $\mathrm{CH}^2_L (\mathfrak{X}) \{p \}$ has positive corank. This also implies that the unramified cohomology group $\mathrm{H}^3_{\mathrm{nr}} (\mathfrak{X}, \mathbb{Q}_p / \mathbb{Z}_p (2))$ is infinite.

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Accepted 14 April 2015

Published 13 April 2016