This paper proves local-global principles for Galois cohomology groups over function fields of curves that are defined over a complete discretely valued field. We show in particular that such principles hold for , for all . This is motivated by work of Kato and others, where such principles were shown in related cases for . Using our results in combination with cohomological invariants, we obtain local-global principles for torsors and related algebraic structures over . 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. 215–253DOI 10.4171/CMH/317