3028indexindex.xmlDeligne's "Hodge Theory I, II, and III"This is an English translation of P. Deligne's three papers on Hodge theory:
"Théorie de Hodge I", Actes du Congrès intern. math. 1 (1970) pp. 425–430.
[PDF]
"Théorie de Hodge II", Pub. Math. de l'IHÉS 40 (1971) pp. 5–58.
[PDF]
"Théorie de Hodge III", Pub. Math. de l'IHÉS 44 (1974) pp. 5–77.
[PDF]TO-DO: replace fref by refThe translator (Tim Hosgood) takes full responsibility for any errors introduced, and claims no rights to any of the mathematical content herein.
You can view the entire source code of this translation (and contribute or submit corrections) in the GitHub repository.
Corrections and comments welcome.Hodge Theory I ✓
Hodge Theory II ✓
Introduction
Filtrations
Filtered objects
Opposite filtrations
The two filtrations lemma
Hypercohomology of filtered complexes
Hodge structures
Pure structures
Hodge theory
Mixed structures
Hodge theory of non-singular algebraic varieties
Logarithmic poles and residues
Mixed Hodge theory
Applications and supplements
The fixed set theorem
The semi-simplicity theorem
Supplement to [D1968]
Homomorphisms of abelian schemes
Hodge Theory III
Introduction ✓
Terminology and notation ✓
Cohomological descent ✓
Simplicial topological spaces
Cohomology of simplicial topological spaces
Cohomological descent
Examples of simplicial topological spaces ✓
Classifying spaces
Construction of hypercovers
Relative cohomology
Multi-simplicial spaces
Supplements to §1 ✓
Filtered derived category
Supplements to the two-filtrations lemma
Hodge theory of algebraic spaces
Hodge complexes
Separated algebraic spaces
Hodge theory of simplicial schemes
Examples and applications
Cohomology of groups and of classifying spaces
Hodge theory of smooth hypersurfaces, following Griffiths
Construction of complexes of first-order differential operators
Hodge theory in level
1-motives
1-motives and bi-extensions
Algebraic interpretation of the mixed : the case of curves
Translation of a theorem of Picard
Bibliography