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Local diophantine properties of modular curves of 𝒟-elliptic sheaves
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Mihran Papikian
Veröffentlicht/Copyright:
19. Juni 2011
Abstract
We study the existence of rational points on modular curves of 𝒟-elliptic sheaves over local fields and the structure of special fibres of these curves. We discuss some applications which include finding presentations for arithmetic groups arising from quaternion algebras, finding the equations of modular curves of 𝒟-elliptic sheaves, and constructing curves violating the Hasse principle.
Received: 2009-12-02
Published Online: 2011-06-19
Published in Print: 2012-03
©[2012] by Walter de Gruyter Berlin Boston
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Artikel in diesem Heft
- Towards the smoothness of optimal maps on Riemannian submersions and Riemannian products (of round spheres in particular)
- The skew-torsion holonomy theorem and naturally reductive spaces
- On the equality between homological and cohomological dimension of groups
- On Néron class groups of abelian varieties
- Multiplicative Diophantine exponents of hyperplanes and their nondegenerate submanifolds
- Local diophantine properties of modular curves of 𝒟-elliptic sheaves
- Uniform vector bundles on Fano manifolds and applications
- Comparison between analytic and algebraic constructions of toroidal compactifications of PEL-type Shimura varieties
- Rigidity of entire self-shrinking solutions to curvature flows
Artikel in diesem Heft
- Towards the smoothness of optimal maps on Riemannian submersions and Riemannian products (of round spheres in particular)
- The skew-torsion holonomy theorem and naturally reductive spaces
- On the equality between homological and cohomological dimension of groups
- On Néron class groups of abelian varieties
- Multiplicative Diophantine exponents of hyperplanes and their nondegenerate submanifolds
- Local diophantine properties of modular curves of 𝒟-elliptic sheaves
- Uniform vector bundles on Fano manifolds and applications
- Comparison between analytic and algebraic constructions of toroidal compactifications of PEL-type Shimura varieties
- Rigidity of entire self-shrinking solutions to curvature flows
