Brauer groups of varieties over local fields of finite characteristic

We show that the non-log version of Kato’s ramification filtration on the Brauer group of a separated and finite type regular scheme over a positive characteristic local field coincides with the evaluation filtration. This extends a recent result of Bright-Newton to positive characteristics. Among several applications, we extend some results of Ieronymou, Saito-Sato and Kai to positive characteristics.