Parabolic Hecke eigensheaves

Chapter 1. Introduction
1.1. The conjecture
1.2. The program
1.3. Parabolic version
1.4. Our results
Chapter 2. Parabolic objects
2.1. Parabolic bundles and Higgs bundles
2.2. Parabolic Chern classes
2.3. Natural operations
2.4. Stability
Chapter 3. Moduli Spaces
3.1. A family of moduli problems
3.2. Birational models and chambers
3.3. The GIT construction
Chapter 4. The Hecke correspondence
4.1. Hecke correspondences of moduli stacks and moduli spaces
4.2. The Hecke correspondence on X
Chapter 5. The modular spectral cover
5.1. The fiber of the Hitchin map
5.2. The base locus
5.3. The case of nilpotent residues
5.4. Wobbly, shaky and exceptional loci
Chapter 6. Hecke eigensheaves
6.1. Parabolic divisors
6.2. Consistent labeling
6.3. Parabolic Hecke data
6.4. The eigensheaf property
6.5. Abelianization
6.6. Linear equivalence conditions
Chapter 7. Solving the constraints
7.1. Chern characters
7.2. Parabolic Chern characters
7.3. Killing the Chern classes
7.4. Hecke conditions
7.5. The class of the kernel
7.6. The Okamoto map
Chapter 8. Summary
TDO and the tamely ramified GLC
A.1. Setup for the tamely ramified GLC
A.2. The non-abelian Hodge theory approach
A.3. Twisted Deligne-Goresky-MacPherson extensions
A.4. Remarks on untwisting
A.5. Geometric class field theory revisited
Bibliography
List of notations
List of notations
Index
Index