Local-global principles for Galois cohomology

2012/08/31 by Harbater, David, Hartmann, Julia, Krashen, Daniel · 1 citation
#11E72 #13F25 #14H25 (Primary) 12G05 #20G15 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1208.6359

Abstract

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 Hⁿ(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.

Cited by

• Mayer--Vietoris sequences for complexes of tori

Related

• Local-global principles for torsors over arithmetic curves
• Local-global questions for tori over p-adic function fields
• Note on linear relations in Galois cohomology and étale K-theory of curves
• Galois Cohomology of Reductive Groups over Function Fields over ℂ((t))
• A comparison between obstructions to local-global principles over semiglobal fields