André-Quillen homology and ascent of complete intersection flat dimensions

Abstract: Using Andr\'{e}-Quillen homology, we prove an ascent result for different types of complete intersection flat dimensions along an essentially of finite type flat local homomorphism with complete intersection closed fiber. As an application of our result, we extend a result of Majadas Soto and of Avramov, Henriques and \c{S}ega on the Andr\'{e}-Quillen dimension of surjective local homomorphisms to that of essentially of finite types.