Arithmetic toric varieties
Algebraic Geometry
2013-05-28 v3 Number Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1003.5141,
title = {Arithmetic toric varieties},
author = {E. Javier Elizondo and Paulo Lima-Filho and Frank Sottile and Zach Teitler},
journal= {arXiv preprint arXiv:1003.5141},
year = {2013}
}
Comments
Revised and streamlined. 31 pages, several figures