INVERSE VALUES OF THE MODULAR j-INVARIANT AND HOMOTOPY LIE THEORY

Abstract

The goal of this article is to give a simple arithmetic application of the enhanced homotopy (Lie) theory for algebraic varieties developed by the second and third authors. Namely, we compute an inverse value of the modular j-invariant by using a deformation theory for period matrices of elliptic curves based on homotopy Lie theory. Another key ingredient in our approach is J. Carlson and P. Griffiths' explicit computation regarding infinitesimal variations of Hodge structures.