2023/02/13 by Krishna, Amalendu, Rathore, Jitendra, Sadhukhan, Samiron
#14F22 #19D45 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14C25 #Secondary 14F30
paper · doi:10.48550/arxiv.2302.06069
We prove duality theorems for the étale cohomology of logarithmic Hodge-Witt sheaves and split tori on smooth curves over a local field of positive characteristic. As an application, we obtain a description of the Brauer group of the function fields of curves over local fields in terms of the characters of the idele groups. We also show that the classical Brauer-Manin pairing between the Brauer and Picard groups of smooth projective curves over local fields has analogues for arbitrary smooth curves, smooth projective curves with modulus and singular projective curves over such fields.