2024/09/11 by Saltman, David J
#Algebraic Geometry (math.AG) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2409.07240
There are two outstanding questions about division algebras of prime degree p. The first is whether they are cyclic, or equivalently crossed products. The second is whether the center, Z(F,p), of the generic division algebra UD(F,p) is stably rational over F. When F is characteristic 0 and contains a primitive p root of one, we show that there is a connection between these two questions. Namely, we show that if Z(F,p) is not stably rational then UD(F,p) is not cyclic.