# A general extension theorem for cohomology classes on non reduced analytic spaces

## TL;DR

This paper extends the Ohsawa-Takegoshi L^2 extension theorem to more general settings, including non-reduced subvarieties and non-compact Kähler manifolds, broadening its applicability in complex geometry.

## Contribution

It generalizes the L^2 extension theorem to singular hermitian line bundles, non-reduced subvarieties, and non-compact Kähler manifolds, expanding the theorem's scope.

## Key findings

- Extended L^2 theorem to singular hermitian line bundles
- Allowed non-reduced subvarieties for extension
- Applicable to non-compact Kähler manifolds

## Abstract

The main purpose of this paper is to generalize the celebrated L${}^2$ extension theorem of Ohsawa-Takegoshi in several directions : the holomorphic sections to extend are taken in a possibly singular hermitian line bundle, the subvariety from which the extension is performed may be non reduced, the ambient manifold is K{\"a}hler and holomorphically convex, but not necessarily compact.