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 \( {H}^{2}(K, \mathbb{Z}/\ell), {l} \neq car.K \). 

    References

    SHOWING 1-10 OF 16 REFERENCES
    Applications of patching to quadratic forms and central simple algebras
    • 80
    • PDF
    Division algebras over surfaces
    • 18
    The u-invariant of the function fields of p-adic curves
    • 51
    • Highly Influential
    • PDF
    A Hasse principle for two dimensional global fields.
    • 176
    Cyclic algebras over p-adic curves
    • 38
    • PDF
    Cohomological Hasse principle and motivic cohomology for arithmetic schemes
    • 41
    • PDF
    Quadratic Forms
    • 29
    • PDF