Mathematical Research Letters

Volume 22 (2015)

Number 5

Torsion in the Lichtenbaum Chow group of arithmetic schemes

Pages: 1491 – 1507



A. Rosenschon (Mathematisches Institut, Ludwig-Maximilians-Universität, München, Germany)

V. Srinivas (School of Mathematics, Tata Institute of Fundamental Research, Mumbai, India)


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.

Accepted 14 April 2015

Published 13 April 2016