Given a (0, p) -mixed characteristic complete discrete valued field K we define a class of finite field extensions called pseudo-perfect extensions such that the natural restriction map on the mod-p Milnor K-groups is trivial for all p 2. This implies that pseudo-perfect extensions split every element in Hⁱ (K, μₚ^ i-1) yielding period-index bounds for Brauer classes as well as higher cohomology classes of K. As a corollary, we prove a conjecture of Bhaskhar-Haase that the Brauer p-dimension of K is upper bounded by n+1 where n is the p-rank of the residue field. When K is the fraction field of a complete regular ring, we show that any p-torsion element in Br (K) that is nicely ramified is split by a pseudo-perfect extension yielding a bound on its index. We then use patching techniques of Harbater, Hartmann and Krashen to show that the Brauer p-dimension of semi-global fields of residual characteristic p is at most n+2. This bound is sharper than previously known in the work of Parimala-Suresh.
S. Srimathy (Sat,) studied this question.