A torsion Jacquet-Langlands correspondence

Acknowledgments
Chapter 1. Introduction
	1.1. Introduction
	1.2. A guide to reading this book
Chapter 2. Some Background and Motivation
	2.1. Reciprocity over Z
	2.2. Inner forms of GL(2): conjectures
Chapter 3. Notation
	3.1. A summary of important notation
	3.2. Fields and adeles
	3.3. The hyperbolic 3-manifolds
	3.4. Homology, cohomology, and spaces of modular forms
	3.5. Normalization of metric and measures
	3.6. S-arithmetic groups
	3.7. Congruence homology
	3.8. Eisenstein classes
	3.9. Automorphic representations. Cohomological representations
	3.10. Newforms and the level raising/level lowering complexes
Chapter 4. Raising the Level: newforms and oldforms
	4.1. Ihara\'s lemma
	4.2. No newforms in characteristic zero.
	4.3. Level raising
	4.4. The spectral sequence computing the cohomology of S-arithmetic groups
	4.5. zeta(-1) and the homology of PGL2
Chapter 5. The split case
	5.1. Noncompact hyperbolic manifolds: height functions and homology
	5.2. Noncompact hyperbolic manifolds: eigenfunctions and Eisenstein series
	5.3. Reidemeister and analytic torsion
	5.4. Noncompact arithmetic manifolds
	5.5. Some results from Chapter 4 in the split case
	5.6. Eisenstein series for arithmetic manifolds: explicit scattering matrices
	5.7. Modular symbols, boundary torsion, and the Eisenstein regulator
	5.8. Comparing Reidmeister and analytic torsion: the main theorems
	5.9. Small eigenvalues
	5.10. The proof of Theorem 5.8.3
Chapter 6. Comparisons between Jacquet-Langlands pairs
	6.1. Notation
	6.2. The classical Jacquet Langlands correspondence
	6.3. Newforms, new homology, new torsion, new regulator
	6.4. Torsion Jacquet-Langlands, crudest form
	6.5. Comparison of regulators and level-lowering congruences: a conjecture
	6.6. Torsion Jacquet-Langlands, crude form: matching volume and congruence homology
	6.7. Essential homology and the torsion quotient
	6.8. Torsion Jacquet-Langlands, refined form: spaces of newforms
	6.9. The general case
Chapter 7. Numerical examples
	7.1. The manifolds
	7.2. No characteristic zero forms
	7.3. Characteristic zero oldforms
	7.4. Characteristic zero newforms and level lowering
	7.5. Eisenstein Deformations: Theoretical Analysis
	7.6. Eisenstein Deformations: Numerical Examples
	7.7. Phantom classes
	7.8. K2 and F = Q(sqrt(-491))
	7.9. Table
Bibliography
Index