10. Hodge theory in level ≤1
10.1 1-motives
Deligne’s Hodge Theory I, II, and III
About this translation
Hodge Theory I
Hodge Theory II
Introduction
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
Hodge Theory III
Introduction
Terminology and notation
5. Cohomological descent
5.1 Simplicial topological spaces
5.2 Cohomology of simplicial topological spaces
5.3 Cohomological descent
6. Examples of simplicial topological spaces
6.1 Classifying spaces
6.2 Construction of hypercovers
6.3 Relative cohomology
6.4 Multi-simplicial spaces
7. Supplements to §1
7.1 Filtered derived category
7.2 Supplements to the two-filtrations lemma
8. Hodge theory of algebraic spaces
8.1 Hodge complexes
8.2 Separated algebraic spaces
8.3 Hodge theory of simplicial schemes
9. Examples and applications
9.1 Cohomology of groups and of classifying spaces
9.2 Hodge theory of smooth hypersurfaces, following Griffiths
9.3 Construction of complexes of first-order differential operators
10. Hodge theory in level ≤1
10.1 1-motives
10.2 1-motives and bi-extensions
10.3 Algebraic interpretation of the mixed
\mathrm{H}^1
: the case of curves
10.4 Translation of a theorem of Picard
10. Hodge theory in level ≤1
10.1 1-motives
10.1 1-motives
9.3 Construction of complexes of first-order differential operators
10.2 1-motives and bi-extensions