Let F be a p-adic field, that is, a finite extension of . Let D be a finite dimensional division algebra over F, and let be the group of elements of reduced norm 1 in D. Prasad and Raghunathan proved that is a cyclic p-group whose order is bounded from below by the number of p-power roots of unity in F, unless D is a quaternion algebra over . In this paper we give an explicit upper bound for the order of for and determine precisely when F is cyclotomic, , and the degree of D is not a power of p.
(with an appendix written by MIKHAIL ERSHOV AND THOMAS WEIGEL)
To Gopal Prasad on the occasion of his 75th birthday
"On the Second Cohomology of the Norm One Group of a p-Adic Division Algebra." Michigan Math. J. 72 261 - 330, August 2022. https://doi.org/10.1307/mmj/20217210