Shafarevich conjecture for complete intersections

Let $K$ be a number field, let $S$ be a finite set of finite places of $K$, and let $T$ be a type. A smooth complete intersection of type $T$ over $K$ has good reduction outside $S$ if it has good reduction at every finite place of $K$ not in $S$.

Shafarevich conjecture for complete intersections. The set of $K$-linear isomorphism classes of smooth complete intersections of type $T$ over $K$ with good reduction outside $S$ is finite.

This generalizes the Shafarevich finiteness philosophy from curves and abelian varieties to complete intersections. The paper proves this statement in important cases, but the displayed general formulation is presented as a conjecture.