Periods for flat algebraic connections

TL;DR

This paper generalizes a duality between algebraic de Rham cohomology and rapid decay homology for flat algebraic connections from surfaces to arbitrary dimensions, leveraging recent advances by Mochizuki.

Contribution

It extends the duality results to higher dimensions using Mochizuki's recent proof, broadening the scope of previous work on algebraic connections.

Findings

Duality between algebraic de Rham cohomology and rapid decay homology established in higher dimensions.

Verification that Mochizuki's results enable this generalization.

Theoretical framework applicable to smooth quasi-projective varieties of any dimension.

Abstract

In previous work, 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, which has been proved recently by T. Mochizuki for algebraic connections in any dimension. In the present article, we verify that Mochizuki's results allow to generalize these duality results to arbitrary dimensions also.