 Grothendieck existence theorem

The Grothendieck Existence Theorem is a fundamental result in algebraic geometry that pertains to the construction of schemes and their coherent sheaves, particularly in the context of the development of the theory of stacks and the Grothendieck topology. In more detail, the theorem addresses the existence of certain kinds of algebraic objects, providing conditions under which a given formal object can be realized by a certain kind of "concrete" object.