Generalization of the theory of mixed Hodge structures and its application

TL;DR

This paper generalizes Deligne's theory of mixed Hodge structures, creating a new subcategory where certain Ext groups are non-zero, revealing deeper structural properties.

Contribution

It introduces a generalized category of mixed Hodge structures with non-vanishing Ext^2 groups, expanding the theoretical framework.

Findings

Established a new subcategory GMHS within mixed Hodge structures.

Proved that Ext_{GMHS}^2(Q,-) can be non-zero in this new setting.

Enhanced understanding of the extension groups in Hodge theory.

Abstract

In this paper, we shall generalize the theory of mixed Hodge structures due to Deligne and obtain a subcategory GMHS in the category of mixed Hodge structures such that we have Ext_{GMHS}^2(Q,-)\not=0 in general.