Unfortunately, I cannot review this paper for Advances in Mathematics. One reason is that
I have enough reviewing job taken upon myself already and do not have enough time in
these later days.
Another reason is that, contrary to what you are saying, I cannot be of any assistance in
determining whether a particular submission is appropriate for publication in Advances.
Whatever my mathematical expertise may or may not be, such a phenomenon as
the high standards of Advances in Mathematics is certainly above my limited capacity of
understanding matters. I've already had one paper rejected by Advances after my
positive review several years ago, and more recently, had my own paper rejected by
Advances with the referee's remarks that my work is "clear and original" but "not yet
ready for publication in Advances in Mathematics".
I have no idea what being a paper "appropriate for publication in Advances in Mathematics"
might consist in.
Sorry for being unable to help,