Coherence of direct images of the De Rham complex

TL;DR

This paper proves the coherence of direct images of the De Rham complex under flat holomorphic maps, introducing a new bi-dg-algebra called the Koszul-De Rham algebra to achieve this result.

Contribution

It develops the Koszul-De Rham algebra, a novel bi-dg-algebra, to establish coherence of direct images of the De Rham complex in complex geometry.

Findings

Proves coherence of direct images of the De Rham complex

Introduces the Koszul-De Rham algebra

Establishes new techniques for complex geometric analysis

Abstract

We show the coherence of the direct images of the De Rham complex relative to a flat holomorphic map with suitable boundary conditions. For this purpose, a notion of bi-dg-algbera called the Koszul-De Rham algbera is dveloped.