On a local-global principle for H³ of function fields of surfaces over a finite field

2013/08/15 by Alena Pirutka, Pirutka, Alena
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1308.3458

arxiv created 2013/08/15 · arxiv updated 2013/08/16

Abstract

Let K be the function field of a smooth projective surface over a finite field. In this article, following the work of Parimala and Suresh, we establish a local-global principle for the divisibility of elements in H³(K,Z/l) by elements in H²(K,Z/l).

Related

• Degree three cohomology of function fields of surfaces
• A comparison between obstructions to local-global principles over semiglobal fields
• The local-global principle for divisibility in CM elliptic curves
• Local-global principles for Galois cohomology
• On the minimal set for counterexamples to the local-global principle