On the Termination of Flips for Log Canonical Generalized Pairs

Termination of threefold flips in mixed characteristic

“…In general, this final step can be a very delicate procedure, see, for instance, [3, Section 3] for a recent characteristic 0 proof in this vein, and it is this that presents the barrier in mixed and positive characteristic. We take a slightly different approach, instead making the observation that in fact terminal pairs admit no flips over some open set of a positive dimensional base.…”