On a local-global principle for $H^3$ of function fields of surfaces over a finite field

TL;DR

This paper proves a local-global principle for the divisibility of elements in the third Galois cohomology group of function fields of surfaces over finite fields, extending previous work by Parimala and Suresh.

Contribution

It establishes a new local-global principle for H^3 of function fields of surfaces over finite fields, building on and extending prior results.

Findings

Proves a local-global principle for H^3(K,Z/l) divisibility

Extends the work of Parimala and Suresh

Provides new tools for understanding cohomological properties of function fields

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 H^3(K,Z/l) by elements in H^2(K,Z/l).