Katz–Lang finiteness theorem

The Katz–Lang finiteness theorem is a result in algebraic geometry, specifically in the area of algebraic stacks and their cohomology. It provides conditions under which the set of isomorphism classes of certain algebraic objects can be shown to be finite. The theorem primarily concerns the situation involving stable maps to a projective variety (often referred to as the target variety), and it is particularly important in the context of counting curves.