We study toric varieties over a field k that split in a Galois extension K / k using Galois cohomology with coefficients in the toric automorphism group. Part of this Galois cohomology fits into an exact sequence induced by the presentation of the class group of the toric variety. This perspective helps to compute the Galois cohomology, particularly for cyclic Galois groups. We use Galois cohomology to classify k-forms of projective spaces when K / k is cyclic, and we also study k-forms of surfaces.
This is the accepted version of the following article: Elizondo, E. Javier; Lima-Filho, Paulo; Sottile, Frank; and Teitler, Zach. (2014). "Arithmetic Toric Varieties". Mathematische Nachrichten, 287(2-3), 216-241, which has been published in final form at doi: 10.1002/mana.201200305
E. Javier Elizondo, Paulo Lima-Filho, Frank Sottile and Zach Teitler. "Arithmetic Toric Varieties" Mathematische Nachrichten
Available at: http://works.bepress.com/zach_teitler/19/