Abramovich–Karu's semistable reduction conjecture

Let $f\colon X\rightarrow B$ be a dominant morphism of finite type of integral qe schemes. A morphism is semistable when, in the characteristic-zero setting, its source and target are regular and it has the prescribed monomial local form described in the surrounding setup. Abramovich–Karu's semistable reduction conjecture. There is a projective alteration $B' \rightarrow B$, and a projective modification $X'\rightarrow (X\times_B B')^{\rm pr}$ such that $f'\colon X' \rightarrow B'$ is semistable. This is the proposed strongest form of relative resolution for dominant morphisms, extending semistable reduction beyond curves; the paper studies the conjecture and its polyhedral analogue.