Arthur Packets for p-Adic Groups by Way of Microlocal Vanishing Cycles of Perverse Sheaves, with Examples.

Cover
Title page
Acknowledgments
Chapter 1. Introduction
1.1. Motivation
1.2. Background
1.3. Main results
1.4. Conjecture
1.5. Examples
1.6. Relation to other work
1.7. Disclaimer
Part 1. Arthur packets and microlocal vanishing cycles
Chapter 2. Overview
Chapter 3. Arthur packets and pure rational forms
3.1. Local Langlands group
3.2. L-groups
3.3. Semisimple, elliptic and hyperbolic elements in L-groups
3.4. Langlands parameters
3.5. Arthur parameters
3.6. Langlands parameters of Arthur type
3.7. Pure rational forms
3.8. Langlands packets for pure rational forms
3.9. Arthur packets for quasisplit symplectic or special orthogonal groups
3.10. Arthur packets for inner rational forms
3.11. Pure Arthur packets
3.12. Virtual representations of pure rational forms
Chapter 4. Equivariant perverse sheaves on parameter varieties
4.1. Infinitesimal parameters
4.2. Vogan varieties
4.3. Parameter varieties
4.4. Equivariant perverse sheaves
4.5. Equivariant perverse sheaves on parameter varieties
4.6. Langlands component groups as equivariant fundamental groups
Chapter 5. Reduction to unramified hyperbolic parameters
5.1. Unramification
5.2. Elliptic and hyperbolic parts of the image of Frobenius
5.3. Construction of the unramified parameter
5.4. Construction of the cocharacter
5.5. Proof of Theorem 5.1
5.6. Further properties of Vogan varieties
Chapter 6. Arthur parameters and the conormal bundle
6.1. Regular conormal vectors
6.2. Cotangent space to the Vogan variety
6.3. Conormal bundle to the Vogan variety
6.4. Orbit duality
6.5. Strongly regular conormal vectors
6.6. From Arthur parameters to strongly regular conormal vectors
6.7. Arthur component groups as equivariant fundamental groups.

6.8. Proof of Proposition 6.1
6.9. Equivariant Local systems
Chapter 7. Microlocal vanishing cycles of perverse sheaves
7.1. Background on vanishing cycles
7.2. Calculating vanishing cycles
7.3. Brylinski's functor Ev
7.4. Stalks
7.5. Support
7.6. Open orbit
7.7. Purity and rank on the open orbit
7.8. Perversity
7.9. Restriction to generic elements
7.10. Normalization of Ev
7.11. Remarks on stratified Morse theory and microlocalization
Chapter 8. Arthur packets and ABV-packets
8.1. ABV-packets
8.2. Virtual representations attached to ABV-packets
8.3. Conjecture on Arthur packets
8.4. A basis for stable invariant distributions
Part 2. Examples
Chapter 9. Overview
Chapter 10. Template for the examples
10.1. Arthur packets
10.2. Vanishing cycles of perverse sheaves
10.3. ABV-packets
10.4. Endoscopy and equivariant restriction of perverse sheaves
Chapter 11. SL(2) 4-packet of quadratic unipotent representations
11.1. Arthur packets
11.2. Vanishing cycles of perverse sheaves
11.3. ABV-packets
11.4. Endoscopy and equivariant restriction of perverse sheaves
Chapter 12. SO(3) unipotent representations, regular parameter
12.1. Arthur packets
12.2. Vanishing cycles of perverse sheaves
12.3. ABV-packets
12.4. Endoscopy and equivariant restriction of perverse sheaves
Chapter 13. PGL(4) shallow representations
13.1. Arthur packets
13.2. Vanishing cycles of perverse sheaves
13.3. ABV-packets
13.4. Endoscopy and equivariant restriction of perverse sheaves
Chapter 14. SO(5) unipotent representations, regular parameter
14.1. Arthur packets
14.2. Vanishing cycles of perverse sheaves
14.3. ABV-packets
14.4. Endoscopy and equivariant restriction of perverse sheaves
Chapter 15. SO(5) unipotent representations, singular parameter.

15.1. Arthur packets
15.2. Vanishing cycles of perverse sheaves
15.3. ABV-packets
15.4. Endoscopy and equivariant restriction of perverse sheaves
Chapter 16. SO(7) unipotent representations, singular parameter
16.1. Arthur packets
16.2. Vanishing cycles of perverse sheaves
16.3. ABV-packets
16.4. Endoscopy and equivariant restriction of perverse sheaves
16.5. Tables for the SO(7) example
Bibliography
Index
Back Cover.