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Hilbert modular forms : mod p and p-adic aspects /
Introduction Notations Moduli spaces of abelian varieties with real multiplication Properties of $\mathcal{G}$ Hilbert modular forms The $q$-expansion map The partial Hasse invariants Reduceness of the partial Hasse invariants A compactification of $\mathfrak{M} (k, \mu_{pN})^{\rm{Kum}}$ Congruences...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, RI :
American Mathematical Society,
2005.
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| Colección: | Memoirs of the American Mathematical Society ;
no. 819. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.