  It is proposed that certain techniques from arithmetic algebraic geometry
provide a framework which is useful to formulate a direct and intrinsic link
between the geometry of Calabi-Yau manifolds and the underlying conformal field
theory. Specifically it is pointed out how the algebraic number field
determined by the fusion rules of the conformal field theory can be derived
from the number theoretic structure of the cohomological Hasse-Weil L-function
determined by Artin's congruent zeta function of the algebraic variety. In this
context a natural number theoretic characterization arises for the quantum
dimensions in this geometrically determined algebraic number field.
