  This article explores possible embeddings of the Standard Model gauge group
and its matter representations into F-theory. To this end we construct elliptic
fibrations with gauge group SU(3)xSU(2)xU(1)xU(1) as suitable restrictions of a
${\rm Bl}_2{\mathbb P}^2$-fibration with rank-two Mordell-Weil group. We
analyse the five inequivalent toric enhancements to gauge group SU(3)xSU(2)
along two independent divisors W_3 and W_2 in the base. For each of the
resulting smooth fibrations, the representation spectrum generically consists
of a bifundamental (3,2), three types of (1,2) representations and five types
of (3,1) representations (plus conjugates), in addition to charged singlet
states. The precise spectrum of zero-modes in these representations depends on
the 3-form background. We analyse the geometrically realised Yukawa couplings
among all these states and find complete agreement with field theoretic
expectations based on their U(1) charges. We classify possible identifications
of the found representations with the Standard Model field content extended by
right-handed neutrinos and extra singlets. The linear combination of the two
abelian gauge group factors orthogonal to hypercharge acts as a selection rule
which, depending on the specific model, can forbid dangerous dimension-four and
-five proton decay operators.
