Periods for flat algebraic connections

Abstract

In previous work (Hien, Math. Ann. 337, 631-669, 2007), we established a duality between the algebraic de Rham cohomology of a flat algebraic connection on a smooth quasi-projective surface over the complex numbers and the rapid decay homology of the dual connection relying on a conjecture by C. Sabbah. In the present article, we generalize this result to arbitrary dimensions unconditionally using recent results of T. Mochizuki.