2010/03/26 by E. Javier Elizondo, Elizondo, E. Javier, Paulo Lima‐Filho +5
Computer Science · Mathematics · #11E72 #14M25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1003.5141
openalex publication_date 2010/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.