Following Baldwin-Eklof-Trlifaj, a pair P = (A,<) is called an abstract elementary class (AEC) of roots of Ext provided (1) A is a left-hand class of a hereditary cotorsion pair, that is, there is a class of modules C, such that A = { M \in Mod-R ; Ext^i_R(M,N) = 0 for all i > 0 and all N \in C }, and (2) if X, Y in A are such that X is a submodule of Y, then X < Y, iff X/Y \in A. There is an interesting interplay between homological properties of the classes C and A, and model-theoretic properties of P. Applying it, one can for example prove that if P admits intersections, then P has finite character. We will also prove Shelah’s Categoricity Conjecture for the particular setting of AEC’s of roots Ext.