On the behaviour of Brauer p-dimensions under finitely-generated field extensions

The present paper shows that if q∈Pq∈P or q=0q=0, where PP is the set of prime numbers, then there exist characteristic q   fields Eq,k:k∈NEq,k:k∈N, of Brauer dimension Brd(Eq,k)=kBrd(Eq,k)=k and infinite absolute Brauer p  -dimensions abrdp(Eq,k)abrdp(Eq,k), for all p∈Pp∈P not dividing q2−qq2−q. This ensures that Brdp(Fq,k)=∞Brdp(Fq,k)=∞, p†q2−qp†q2−q, for every finitely-generated transcendental extension Fq,k/Eq,kFq,k/Eq,k. We also prove that each sequence ap,bpap,bp, p∈Pp∈P, satisfying the conditions a2=b2a2=b2 and 0≤bp≤ap≤∞0≤bp≤ap≤∞, equals the sequence abrdp(E),Brdp(E)abrdp(E),Brdp(E), p∈Pp∈P, for a field E of characteristic zero.