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Hilbert modular forms: mod $p$ and $p$-adic aspects
About this Title
F. Andreatta and E. Z. Goren
Publication: Memoirs of the American Mathematical Society
Publication Year:
2005; Volume 173, Number 819
ISBNs: 978-0-8218-3609-5 (print); 978-1-4704-0420-8 (online)
DOI: https://doi.org/10.1090/memo/0819
MathSciNet review: 2110225
MSC: Primary 11F41; Secondary 11F33, 11F85
Table of Contents
Chapters
- 1. Introduction
- 2. Notations
- 3. Moduli spaces of abelian varieties with real multiplication
- 4. Properties of $\mathcal {G}$
- 5. Hilbert modular forms
- 6. The $q$-expansion map
- 7. The partial Hasse invariants
- 8. Reduceness of the partial Hasse invariants
- 9. A compactification of $\mathfrak {M}(k, \mu _{pN})^{Kum}$
- 10. Congruences mod $p^n$ and Serre’s $p$-adic modular forms
- 11. Katz’s $p$-adic Hilbert modular forms
- 12. The operators $\Theta _{\mathfrak {P},i}$
- 13. The operator $V$
- 14. The operator $U$
- 15. Applications to filtrations of modular forms
- 16. Theta cycles and parallel filtration (inert case)
- 17. Functorialities
- 18. Integrality and congruences for values of zeta functions
- 19. Numerical examples
- 20. Comments regarding values of zeta functions