Hilbert modular forms : [electronic resource] mod p and p-adic aspects / F. Andreatta, E.Z. Goren.

By: Andreatta, F. (Fabrizio), 1972-Contributor(s): Goren, Eyal Z. (Eyal Zvi), 1963-Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v. 819Publication details: Providence, RI : American Mathematical Society, 2005Description: 1 online resource (vi, 100 p. : ill.)ISBN: 9781470404208 (online)Subject(s): Arithmetical algebraic geometry | Hilbert modular surfaces | Forms, Modular | Moduli theoryAdditional physical formats: Hilbert modular forms :DDC classification: 510 s | 516.3/5 LOC classification: QA3 | .A57 no. 819 | QA242.5Online resources: Contents | Contents
Contents:
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
Item type: E-BOOKS
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Link to resource Available EBK13272

"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

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

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