Local diophantine properties of modular curves of 𝒟-elliptic sheaves

DOI10.1515/CRELLE.2011.104zbMath1296.11082arXiv1006.3237OpenAlexW2040539809MaRDI QIDQ2879870

Mihran Papikian

Publication date: 5 April 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/1006.3237

zbMATH Keywords

Hasse principlemodular curvearithmetic group\(\mathcal D\)-elliptic sheaves

Mathematics Subject Classification ID

Local ground fields in algebraic geometry (14G20) Varieties over finite and local fields (11G25)

Related Items

On component groups of Jacobians of quaternionic modular curves ⋮ Maximal orders containing a given sub-order for local fields of even characteristic ⋮ \(\mathcal D\)-elliptic sheaves and odd Jacobians ⋮ On genera containing non-split Eichler orders over function fields ⋮ Representation fields for orders of small rank ⋮ Computing quaternion quotient graphs via representations of orders ⋮ On Jacquet-Langlands isogeny over function fields ⋮ Drinfeld-Stuhler modules

Cites Work

• The class number of hereditary orders in non-Eichler algebras over global function fields
• Local diophantine properties of Shimura curves
• On the Hasse principle for Shimura curves
• Genus formula for modular curves of \(\mathcal D\)-elliptic sheaves
• On hyperelliptic modular curves over function fields
• On the real points of an arithmetic quotient of a bounded symmetric domain
• \({\mathcal D}\)-elliptic sheaves and the Langlands correspondence
• Curves with infinitely many points of fixed degree
• Galois properties of points of finite order of elliptic curves
• Endomorphisms of exceptional \(\mathcal{D}\)-elliptic sheaves

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