Characterising local fields of positive characteristic by Galois theory and the Brauer group

We show that each local field F<i>q</i>((<i>t</i>)) of characteristic <i>p</i> &gt; 0 is characterised up to<br/>isomorphism within the class of all fields of imperfect exponent at most 1 by (certain small quotients of) its absolute Galois group together with natural axioms concerning the p-torsion of its Brauer group. This complements previous work by Efrat–Fesenko, who analysed fields whose absolute Galois group is isomorphic to that of a local field of characteristic <i>p</i>.