  In this paper the problem of constructing spacetime from string theory is
addressed in the context of D-brane physics. It is suggested that the knowledge
of discrete configurations of D-branes is sufficient to reconstruct the motivic
building blocks of certain Calabi-Yau varieties. The collections of D-branes
involved have algebraic base points, leading to the notion of K-arithmetic
D-crystals for algebraic number fields K. This idea can be tested for D0-branes
in the framework of toroidal compactifications via the conjectures of Birch and
Swinnerton-Dyer. For the special class of D0-crystals of Heegner type these
conjectures can be interpreted as formulae that relate the canonical Neron-Tate
height of the base points of the D-crystals to special values of the motivic
L-function at the central point. In simple cases the knowledge of the
D-crystals of Heegner type suffices to uniquely determine the geometry.
