Hasse Invariant for the Tame Brauer Group of a Higher Local Field

2021/04/04 by Brussel, Eric
#11R52 (Primary) 11S45 #12G05 #16K50 (Secondary) #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2104.01692

Abstract

We generalize the Hasse invariant of local class field theory to the tame Brauer group of a higher dimensional local field, and use it to study the arithmetic of central simple algebras over such fields, which are given \it a priori as tensor products of standard cyclic algebras. We also compute the tame Brauer dimension (or \it period-index bound) and the cyclic length of a general henselian-valued field of finite rank and finite residue field.

Related

• On the Hasse Principle for the Brauer group of a purely transcendental extension field in one variable over an arbitrary field
• Hasse principles for higher-dimensional fields
• Primarily quasilocal fields and 1-dimensional abstract local class field theory
• Symbol length in the Brauer group of a field
• Brauer p-dimension of henselian discretely valued fields over characteristic p>0