2011/06/27 by Rowen, Louis, Saltman, David J
#12G05 #14C22 #14F22 #16K20 #16K50 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1106.5517
This paper began as an investigation of the question of whether D1 ⊗F D2 is a domain where the Di are division algebras and F is an algebraically closed field contained in their centers. We present an example where the answer is "no", and also study the Picard group and Brauer group properties of F1 ⊗F F2 where the Fi are fields. Finally, as part of our example, we have results about division algebras and Brauer groups over curves. Specifically, we give a splitting criterion for certain Brauer group elements on the product of two curves over F.