TITLE: State of resolution in positive characteristic?
QUESTION [21 upvotes]: Heisuke Hironaka's coming talk makes me wonder how the state of the work on that theme is. So far, I noticed (but didn't read) these papers:
Kawanoue, Hiraku, Toward resolution of singularities over a field of positive characteristic. I. Foundation; the language of the idealistic filtration, Publ. Res. Inst. Math. Sci. 43, No. 3, 819-909 (2007). ZBL1170.14012.
Urabe, Tohsuke, New Ideas for Resolution of Singularities in Arbitrary Characteristic.
Edit: Another recent talk by Hironaka (in Vienna).

REPLY [31 votes]: Also, I'd like to point out this paper of Hironaka... 
http://www.math.harvard.edu/~hironaka/pRes.pdf
I haven't read the paper, and also I haven't heard anybody talking about it in the last weeks, which I find a little strange given the problem in question... has anybody here gone through the proof?