1. A method for memory fault management in a virtual storage environment, the virtual storage environment including a base space, a first subspace, and content stored in an auxiliary storage memory physical address, the base space and the first subspace having respective virtual addresses associated with the content stored in the auxiliary storage memory physical address, the method comprising: a computer determining that a fault associated with the base space virtual address has occurred; the computer, in response to determining that the fault associated with the base space virtual address has occurred, copying the content from the auxiliary storage memory physical address to a central storage memory physical address; and the computer updating a hierarchy of dynamic address translation (DAT) tables of the base space to associate the base space virtual address with the central storage memory physical address, while not updating a hierarchy of DAT tables of the first subspace to associate the first subspace virtual address with the central storage memory physical address.