Niveaux de R-scindement de structures de Hodge mixtes

Abstract

We propose a generalization of the notion of $\mathbf{R}$-split mixed Hodge structure by defining a $\mathbf{R}$-splitting level for mixed Hodge structures. This is a discrete invariant taking values in positive integers and equal to 0 for $\mathbf{R}$-split mixed Hodge structures. We describe some properties of this invariant for classical operations on these structures and give some explicit calculation.

25 pages