Journal ArticleDOI
Overconvergent modular sheaves and modular forms for GL 2/F
Reads0
Chats0
TLDR
In this paper, the authors construct p-adic families of overconvergent Hilbert modular forms (of non-necessarily parallel weight) as sections of a Hilbert modular sheaves.Abstract:
Given a totally real field F and a prime integer p which is unramified in F, we construct p-adic families of overconvergent Hilbert modular forms (of non-necessarily parallel weight) as sections of, so called, overconvergent Hilbert modular sheaves. We prove that the classical Hilbert modular forms of integral weights are overconvergent in our sense. We compare our notion with Katz’s definition of p-adic Hilbert modular forms. For F = ℚ, we prove that our notion of (families of) overconvergent elliptic modular forms coincides with those of R. Coleman and V. Pilloni.read more
Citations
More filters
Journal ArticleDOI
p-adic families of Siegel modular cuspforms
TL;DR: In this paper, it was shown that a slope Siegel cuspidal eigenform of genus g can be p-adically deformed over the g-dimensional weight space.
Posted Content
P-Adic families of Siegel modular cuspforms
TL;DR: In this paper, it was shown that a finite slope Siegel cuspidal eigenform of genus g can be p-adically deformed over the g-dimensional weight space.
Journal ArticleDOI
Universal eigenvarieties, trianguline Galois representations, and p-adic Langlands functoriality
David T. Hansen,James Newton +1 more
TL;DR: This article constructed eigenvarieties associated with reductive groups and established some basic geometric properties of these spaces, building on work of Ash-Stevens, Urban, and others, and formulated a precise modularity conjecture linking trianguline Galois representations with overconvergent cohomology classes.
Posted Content
p-adic Cohomology and classicality of overconvergent Hilbert modular forms
Yichao Tian,Liang Xiao +1 more
TL;DR: In this article, it was shown that the rigid cohomology of the ordinary locus has the same image as the classical forms in the Grothendieck group of Hecke modules.
Journal ArticleDOI
The eigencurve over the boundary of weight space
TL;DR: In this paper, the eigencurve associated to a definite quaternion algebra over the boundary annuli of weight space was shown to be a disjoint union of infinitely many connected components each finite and flat over the weight annuli.
References
More filters
Book
Degeneration of Abelian varieties
Gerd Faltings,Ching-Li Chai +1 more
TL;DR: In this article, Mumford's analysis of degenerating Abelian Varieties over complete rings is presented, along with a glossary of notations, and an analytical construction of Degenerating ABVs over complete ring is presented.
Book ChapterDOI
P-ADIC Properties of Modular Schemes and Modular Forms
TL;DR: In this article, a modular form of weight k and level n becomes a section of a certain line bundle, and the reduction modulo p of identical relations which hold over the line bundle is obtained.
Journal ArticleDOI