Local-global principles for Galois cohomology

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