Abstract
We define and study the properties of the category of formal Hodge structure of level ≤n following the ideas of Barbieri-Viale who discussed the case of level ≤1. As an application, we describe the generalized Albanese variety of Esnault, Srinivas, and Viehweg via the group Ext1 in
. This formula generalizes the classical one to the case of proper but not necessarily smooth complex varieties.
Key Words:
2000 Mathematics Subject Classification:
ACKNOWLEDGMENTS
The author would like to thank L. Barbieri-Viale for pointing his attention to this subject and for helpful discussions. The author also thanks A. Bertapelle for many useful comments and suggestions.
Notes
By thick we mean a subcategory closed under kernels, co-kernels, and extensions.
The superscript prp stands for “proper”. In fact, the sharp cohomology objects (3.1) of a proper variety have this property.
By injective resolution of a complex of sheaves A • we mean a quasi isomorphism A • → I •, where I • is a complex of injective objects.
It is possible to replace ℂ with a field k of characteristic zero. In that case, we must assume that there exists a k rational point in order to have FW(Z) defined over k .
Communicated by C. Pedrini.