Hodge Theory II

Deligne, P. “Théorie de Hodge II”.

Publications Mathématiques de l’IHÉS 40 (1971) pp. 5–58.

publications.ias.edu/node/361

Table of contents

1. Filtrations
   • 1.1 Filtered objects
   • 1.2 Opposite filtrations
   • 1.3 The two-filtrations lemma
   • 1.4 Hypercohomology of filtered complexes
2. Hodge structures
   • 2.1 Pure structures
   • 2.2 Hodge theory
   • 2.3 Mixed structures
3. Hodge theory of non-singular algebraic varieties
   • 3.1 Logarithmic poles and residues
   • 3.2 Mixed Hodge theory
4. Applications and supplements
   • 4.1 The fixed set theorem
   • 4.2 The semi-simplicity theorem
   • 4.3 Supplement to [D1968]
   • 4.4 Homomorphisms of abelian schemes