Abelian lattice-ordered groups and a characterization of the maximal spectrum of a Prüfer domain

The concept of z-projectable abelian lattice-ordered group is introduced, and it is shown that every such group G can be identified with the group of global sections of a sheaf G with totally ordered stalks on the co-Zariski space Min G of minimal prime ideals. Semi-projectable abelian l-groups are z-projectable, but not vice versa. The sheaves G as well as the spaces Min G arising from abelian l-groups G are characterized completely. Using Hochster duality and the Jaffard-Ohm correspondence, the results are applied to determine the maximal spectrum of a Prüfer domain and of a Bézout domain.