2024/10/03 by Zhao, Yizhen
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2410.02926
We use Kato's Swan conductor to study the Brauer p-dimension of fields of characteristic p>0. We mainly investigate two types of fields: henselian discretely valued fields and semi-global fields. While investigating the Brauer p-dimension of semi-global fields, we use a Gersten-type sequence to analyse the ramification behavior of a Brauer class in a 2-dimensional regular local ring. Using this result, we give a partial result on the Brauer p-dimension of function fields of algebraic curves over k((t)) with good reduction.