Semistable reduction for families of complex projective varieties

Let $X\to B$ be a surjective morphism of complex projective varieties with geometrically integral generic fiber. A projective alteration is a projective generically finite morphism, and a projective modification is a projective birational morphism. A morphism is semistable when it has the semistable structure described in the paper.

Semistable reduction conjecture. There is a projective alteration $B_1\to B$ and a projective modification $Y\to X\times_B B_1$ such that

$$Y\to B_1$$

is semistable.

This is the ultimate semistable-reduction goal for families with geometrically integral generic fiber. The paper develops weaker and combinatorial forms of reduction, while the asserted statement is not established here.