The global gauge group structure of F-theory compactifications is tied to the embedding of the Mordell—Weil lattice into the Neron—Severi group, also known as the Shioda map. While this has been previously explored in the case of purely non-abelian gauge algebras, I will extend it to the more general case by including u(1)s. In particular, I will discuss phenomenological implications, such as the natural realization of the full Standard Model gauge group or possible implications on the F-theory swampland. Furthermore, I will argue how similar structures are also present in genus-one fibrations without sections.