Arithmetic Toric Varieties

E. Javier Elizondo, Paulo Lima-Filho, Frank Sottile, Zach Teitler

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

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.

Original languageAmerican English
JournalMathematics Faculty Publications and Presentations
StatePublished - 1 Feb 2014

Keywords

  • Galois cohomology
  • toric variety

EGS Disciplines

  • Mathematics

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