2023/10/31 by Wang, Yidi
#11E72 #12E30 (primary) #12G05 #14B12 #14H25 (secondary) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2310.20119
In this manuscript, we present a partial generalization of the field patching technique initially proposed by Harbater-Hartmann to Hensel semi-global fields, i.e., function fields of curves over excellent henselian discretely valued fields. More specifically, we show that patching holds for étale algebras over such fields and a suitable set of overfields. Within this new framework, we further establish a local-global principle for higher degree Galois cohomology groups over Hensel semi-global fields. As an application, we extend a recent result regarding a uniform period-index bound for higher degree Galois cohomology classes by Harbater-Hartmann-Krashen to Hensel semi-global fields. Additionally, we prove such a bound for coefficient groups of non-prime orders.