  We propose a method to compute the exact number of charged localized massless
matter states in an F-theory compactification on a Calabi-Yau 4-fold with
non-trivial 3-form data. Our starting point is the description of the 3-form
data via Deligne cohomology. A refined cycle map allows us to specify concrete
elements therein in terms of the second Chow group of the 4-fold, i.e. rational
equivalence classes of algebraic 2-cycles. We use intersection theory within
the Chow ring to extract from this data a line bundle class on the curves in
the base of the fibration on which charged matter is localized. The associated
cohomology groups are conjectured to count the exact massless spectrum, in
agreement with general patterns in Type IIB compactifications with 7-branes. We
exemplify our approach by calculating the massless spectrum in an SU(5) x U(1)
toy model based on an elliptic 4-fold with an extra section. The explicit
evaluation of the cohomology classes is performed with the help of the
cohomCalg-algorithm by Blumenhagen et al.
