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Hilbert modular forms : mod p and p-adic aspects

Author: F Andreatta; Eyal Z Goren
Publisher: Providence, RI : American Mathematical Society, 2005.
Series: Memoirs of the American Mathematical Society, no. 819.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Studies Hilbert modular forms in characteristic $p$ and over $p$-adic rings. This title describes the kernel and image of the $q$-expansion map and prove the existence of filtration for Hilbert  Read more...

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Document Type: Book
All Authors / Contributors: F Andreatta; Eyal Z Goren
ISBN: 0821836099 9780821836095
OCLC Number: 56493836
Notes: "Volume 173, number 819 (fourth of 5 numbers)."
Description: vi, 100 pages : illustrations ; 26 cm.
Contents: 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 mod $p^n$ and Serre's $p$-adic modular forms Katz's $p$-adic Hilbert modular forms The operators $\Theta_{\mathfrak{P},i}$ The operator $V$ The operator $U$ Applications to filtrations of modular forms Theta cycles and parallel filtration (inert case) Functorialities Integrality and congruences for values of zeta functions Numerical examples Comments regarding values of zeta functions References.
Series Title: Memoirs of the American Mathematical Society, no. 819.
Responsibility: F. Andreatta, E.Z. Goren.

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