Stelzig, Jonas ; Stelzig, Jonas Robin: Double complexes and Hodge structures as vector bundles. 2018
Inhalt
- Introduction
- Double Complexes and Complex Manifolds
- The Isomorphism Type of a Double Complex
- Purity and Strictness
- Rings of Double Complexes
- The Dolbeault Complex
- Blow-up Formulas
- A Counterexample
- Examples of Decompositions of Dolbeault Complexes
- A Proof of Theorem 1.3
- Rees-bundles
- The Many Faces of Mixed Hodge Structures
- Triples of Opposite Filtrations
- Vector Spaces with an Endomorphism
- Representations of a Pro-algebraic Group
- Filtered Equivariant Bundles on P1C
- Equivariant Bundles on P2C
- Equivariant Bundles with Connection on A2C
- Polarisations
- Complements and Applications
- A Direct Construction in the Pure Case
- The Weight Filtration as a Slope Filtration
- Kato's Local Archimedean Height
- Gamma-Factors
- Hodge Structures and Loops
- Appendices
- Equivariant Sheaves, Connections and Local Systems
- The Radon-Penrose Transform
- Two Functional Equations
- Acknowledgements