Canonical subgroups over Hilbert modular varieties

DOI10.1515/CRELLE.2011.149zbMath1264.14038arXiv0905.2383MaRDI QIDQ5894964

Eyal Z. Goren, Payman L. Kassaei

Publication date: 11 October 2012

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.2383

zbMATH Keywords

abelian varietiesmoduli spacesHilbert modular varieties

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35)

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Classicality for small slope overconvergent automorphic forms on some compact PEL Shimura varieties of type C ⋮ ON A PROPERNESS OF THE HILBERT EIGENVARIETY AT INTEGRAL WEIGHTS: THE CASE OF QUADRATIC RESIDUE FIELDS ⋮ UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ARISING FROM HILBERT MODULAR SURFACES ⋮ Foliations on Shimura varieties in positive characteristic ⋮ Overconvergent modular sheaves and modular forms for \(\mathrm{GL}_{2/F}\) ⋮ Diagonal restrictions of \(p\)-adic Eisenstein families ⋮ \(p\)-adic dynamics of Hecke operators on modular curves ⋮ Modularity lifting in parallel weight one ⋮ Kottwitz-Rapoport and \(p\)-rank strata in the reduction of Shimura varieties of PEL type ⋮ UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ATTACHED TO HILBERT MODULAR FORMS MOD  OF WEIGHT 1 ⋮ On canonical subgroups of Hilbert–Blumenthal abelian varieties ⋮ Modularity lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified case ⋮ \(p\)-adic Hilbert modular forms of weight 1

Cites Work

• Values of abelian \(L\)-functions at negative integers over totally real fields
• Companion forms and weight one forms
• Appendix to ``The Iwasawa conjecture for totally real fields by A.Wiles: Arithmetic minimal compactification of the Hilbert-Blumenthal moduli spaces
• Canonical subgroups and p-adic vanishing cycles for abelian varieties
• A gluing lemma and overconvergent modular forms
• The canonical subgroup: a ``subgroup-free approach
• On the reduction of the Hilbert-Blumenthal-moduli schem with Г0 (p)-level structure
• $\mathcal P$-adic modular forms over Shimura curves over totally real fields
• Analytic continuation of overconvergent eigenforms
• The canonical subgroup for families of abelian varieties
• Overconvergent Hilbert modular forms
• Hasse invariants for Hilbert modular varieties
• Classical and overconvergent modular forms

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