# On a Local-Global Principle for H3 of Function Fields of Surfaces over a Finite Field

@article{Pirutka2017OnAL,
title={On a Local-Global Principle for H3 of Function Fields of Surfaces over a Finite Field},
author={Alena Pirutka},
journal={arXiv: Number Theory},
year={2017},
pages={219-230}
}
• Alena Pirutka
• Published 2017
• Mathematics
• arXiv: Number Theory
• Let K be the function field of a smooth projective surface S over a finite field $$\mathbb{F}$$. In this article, following the work of Parimala and Suresh, we establish a local-global principle for the divisibility of elements in $${H}^{3}(K, \mathbb{Z}/\ell)$$ by elements in $${H}^{2}(K, \mathbb{Z}/\ell), {l} \neq car.K$$.