JournalscmhVol. 89, No. 1pp. 215–253

Local-global principles for Galois cohomology

  • David Harbater

    University of Pennsylvania, Philadelphia, United States
  • Julia Hartmann

    RWTH Aachen, Germany
  • Daniel Krashen

    University of Georgia, Athens, USA
Local-global principles for Galois cohomology cover
Download PDF

Abstract

This paper proves local-global principles for Galois cohomology groups over function fields FF of curves that are defined over a complete discretely valued field. We show in particular that such principles hold for Hn(F,Z/mZ(n1))H^n(F, \mathbb Z/m \mathbb Z(n-1)), for all n>1n>1. This is motivated by work of Kato and others, where such principles were shown in related cases for n=3n=3. Using our results in combination with cohomological invariants, we obtain local-global principles for torsors and related algebraic structures over FF. Our arguments rely on ideas from patching as well as the Bloch–Kato conjecture.

Cite this article

David Harbater, Julia Hartmann, Daniel Krashen, Local-global principles for Galois cohomology. Comment. Math. Helv. 89 (2014), no. 1, pp. 215–253

DOI 10.4171/CMH/317