Automorphic cohomology, motivic cohomology, and the adjoint L-function

Chapter 1. Introduction
1.1. Cohomological representations
1.2. The conjecture
1.3. The case of tori
1.4. Numerical predictions and evidence for the conjecture
1.5. Some problems and questions
1.6. Notation
Chapter 2. Motivic cohomology and Beilinson's conjecture
2.1. Beilinson's conjecture for motives
2.2. Polarizations, weak polarizations and volumes
Chapter 3. Fundamental Cartan and tempered cohomological representations
3.1. First construction of aG* via fundamental Cartan subalgebra
3.2. Second construction of aG* via the dual group
3.3. The tempered cohomological parameter
3.4. The action of the exterior algebra * aG* on the cohomology of a tempered representation
3.5. Metrization
Chapter 4. The motive of a cohomological automorphic representation: conjectures and descent of the coefficient field
4.1. The example of a fake elliptic curve
4.2. The conjectures
Chapter 5. Formulation of the main conjecture
5.1. The Beilinson regulator
5.2. Trace forms
5.3. Review of cohomological automorphic forms
5.4. Formulation of main conjecture
5.5. Properties of the aG* action
Chapter 6. Period integrals
6.1.
6.2. Setup on submanifolds
6.3.
6.4. Setup on automorphic representations and differential forms
6.5. Tamagawa measure versus Riemannian measure
6.6. Lattices inside Lie algebras
6.7. Factorization of measures on G
6.8. Tamagawa factors
6.9. Cohomological periods versus automorphic periods
6.10. Working hypotheses on period integrals
6.11. Summary
Chapter 7. Compatibility with the Ichino-Ikeda conjecture
7.1. Motivic cohomology; traces and metrics and volumes
7.2.
Chapter 8. Hodge linear algebrarelated to the Ichino-Ikeda conjecture
8.1. Preliminaries
8.2. Period invariants of motives
8.3. The case of PGLn PGLn+1 over Q
8.4. The case PGLn PGLn+1 over imaginary quadratic E
8.5. Polarizations
8.6. SO2n SO2n+1 over E imaginary quadratic
8.7. SO2n+1 SO2n+2 over E imaginary quadratic
8.8. Motives with coefficients
Chapter 9. A case with =3
9.1. Notation and assumptions
9.2. Volumes and functoriality
9.3. Analytic torsion and equivariant analytic torsion. The theorems of Moscovici-Stanton and Lipnowski
9.4. Volumes of cohomology groups for Y and
9.5. Proof of Prediction 1.4.3
9.6. Computation of volH3 and volH1
9.7. Proof of the remainder of Theorem 9.11
The motive of a cohomological automorphic representation
A. The notion of a G"0362G-motive
B. The G"0362G motive attached to a cohomological automorphic representation
C. Descent of the coefficient field for a G"0362G-motive
D. Standard representations of the C-group for PGL and SO
Bibliography