Arithmetic toric varieties

Details Arithmetic toric varieties Arithmetic toric varieties

2010-03-26

arxiv.org/abs/1003.5141v1

Mathematics

Algebraic Geometry

27 pages, several figures

Scientific paper

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. 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 classify k-forms of surfaces.

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