Rings of definition of smooth and proper dg-algebras

Abstract

This is a companion paper to math.AT/0609762. For a filtered colimit of commutative rings k=colim k_i, we prove that the homotopy theory of smooth and proper dg-algebras over k is the colimit of the homotopy theories of smooth and proper dg-algebras over k_i. As a consequence, we deduce that any smooth and proper dg-algebra can be defined over a commutative Z-algebra of finite type.