Arithmetic toric varieties |
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| Authors: | E. Javier Elizondo Paulo Lima‐Filho Frank Sottile Zach Teitler |
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| Affiliation: | 1. Instituto de Matemáticas, Universidad Nacional Autónoma de México, área de la Inv. Científica, Circuito Exterior, Ciudad Universitaria, México, México;2. Department of Mathematics, Texas A&M University, Texas, USA;3. Department of Mathematics, Boise State University, Boise, USA |
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| Abstract: | We study toric varieties over a field k that split in a Galois extension  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  is cyclic, and we also study k‐forms of surfaces. |
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| Keywords: | Toric variety Galois cohomology 14M25 11E72 |
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