On the class group of integer-valued polynomial rings over Krull domains

Let D be a Krull domain with quotient field K. We study the class group of the integer-valued polynomial ring over D, Int(D) {f K[X]; f(D) D}. In particular, we give necessary and sufficient conditions on D for the class group of Int(D) to be generated by the classes of the t-invertible t-prime ideals and, in this case, we describe its generators. A case of particular interest is when D is a UFD. We also characterize Krull domains D for which Int(D) is a GCD-domain.