TY  - BOOK
AU  - Andreatta,F.
AU  - Goren,Eyal Z.
TI  - Hilbert modular forms: mod p and p-adic aspects 
T2  - Memoirs of the American Mathematical Society, 
SN  - 9781470404208 (online)
AV  - QA3QA242.5 .A57 no. 819
U1  - 510 s516.3/5 22
PY  - 2005///
CY  - Providence, RI
PB  - American Mathematical Society
KW  - Arithmetical algebraic geometry
KW  - Hilbert modular surfaces
KW  - Forms, Modular
KW  - Moduli theory
N1  - "Volume 173, number 819 (fourth of 5 numbers)."; Includes bibliographical references (p. 98-100); 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; Access is restricted to licensed institutions; Electronic reproduction; Providence, Rhode Island; American Mathematical Society; 2012
UR  - http://www.ams.org/memo/0819
UR  - http://dx.doi.org/10.1090/memo/0819
ER  -