  In this paper, we will study the arithmetic geometry of rank-2 attractors,
which are Calabi-Yau threefolds whose Hodge structures admit interesting
splits. We will develop methods to analyze the algebraic de Rham cohomologies
of rank-2 attractors, and we will illustrate how our methods work by focusing
on an example in a recent paper by Candelas, de la Ossa, Elmi and van Straten.
We will look at the interesting connections between rank-2 attractors in string
theory and Deligne's conjecture on the special values of $L$-functions. We will
also formulate several open questions concerning the potential connections
between string theory and number theory.
