2013/05/14 by Eva Bayer-Fluckiger, Eva Bayer‐Fluckiger, Bayer-Fluckiger, Eva +5
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1305.3161
To appear in Documenta Mathematica
arxiv created 2013/05/14 · openalex publication_date 2013/05/14 · arxiv updated 2013/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let k be a global field of characteristic not 2. The classical Hasse-Minkowski theorem states that if two quadratic forms become isomorphic over all the completions of k, then they are isomorphic over k as well. It is natural to ask whether this is also true for G-quadratic forms, where G is a finite group. In the case of number fields the Hasse principle for G-quadratic forms does not hold in general, as shown by Jorge Morales. The aim of this paper is to study this question when k is a global field of positive characteristic. We give a sufficient criterion for the Hasse principle to hold, and also counter examples : note that these are of different nature than those for number fields.