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| From 22-26 July 2013 there will be a [[http://www.lorentzcenter.nl/|Lorentz Center]] workshop on Arithmetic Geometry in Sage. There will be three main projects during this week. | From 22-26 July 2013 there will be a [[http://www.lorentzcenter.nl/|Lorentz Center]] workshop on Arithmetic Geometry in Sage. There will be four main projects during this week. |
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| * The first project is to enhance the function field functionality of Sage. In particular, it is important to have algorithms for computing with Jacobians of algebraic curves. It is desirable to implement two different frameworks, each with its own advantages: one developed by F. Hess and the other developed by K. Khuri-Makdisi. This project is motivated by the other two projects. | * The first project is to speed up operations with finite fields in Sage. Faster finite fields will mean that the algorithms in the other projects will also be significantly faster. According to [[https://groups.google.com/forum/#!msg/sage-nt/4tu8csrrWJo/gxY95f8s5FkJ|a Google groups discussion]] it should be relatively easy to speed up operations in finite fields of cardinality larger than 2^16 by a factor of 10. If you are interested in working on this, please let us know. |
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| * The second project is to work on practical implementations of the algorithm described in [[http://press.princeton.edu/titles/9491.html|Edixhoven, Couveignes, Bosman, de Jong, and Merkl]] for computing Galois representations over finite fields attached to modular forms. | * The second project is to enhance the function field functionality of Sage. In particular, it is important to have algorithms for computing with Jacobians of algebraic curves. It is desirable to implement two different frameworks, each with its own advantages: one developed by F. Hess and the other developed by K. Khuri-Makdisi. This project is motivated by the following two projects. |
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| * The third project is to work on computing semi-stable models of curves over local fields. The goal is a practical implementation of the algorithms that follow from the new proof of Deligne and Mumford's stable reduction theorem in: K. Arzdorf and S. Wewers, A local proof of the semistable reduction theorem ([[http://arxiv.org/abs/1211.4624|in preparation]]). | * The third project is to work on practical implementations of the algorithm described in [[http://press.princeton.edu/titles/9491.html|Edixhoven, Couveignes, Bosman, de Jong, and Merkl]] for computing Galois representations over finite fields attached to modular forms. |
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| * A possible fourth project might be to speed up operations with finite fields in Sage. Faster finite fields will mean that the algorithms in the other projects will also be significantly faster. According to [[https://groups.google.com/forum/#!msg/sage-nt/4tu8csrrWJo/gxY95f8s5FkJ|a Google groups discussion]] it should be relatively easy to speed up operations in finite fields of cardinality larger than 2^16 by a factor of 10. If you are interested in working on this, please let us know. | * The fourth project is to work on computing semi-stable models of curves over local fields. The goal is a practical implementation of the algorithms that follow from the new proof of Deligne and Mumford's stable reduction theorem in: K. Arzdorf and S. Wewers, A local proof of the semistable reduction theorem, [[http://arxiv.org/abs/1211.4624|arXiv:1211.4624]]. This is worked out for superelliptic curves (''y^n^'' = ''f''(''x'') with ''n'' not divisible by the residue characteristic) by I. Bouw and S. Wewers, Computing ''L''-functions and semistable reduction of superelliptic curves, [[http://arxiv.org/abs/1211.4459|arXiv:1211.4459]]. |
Sage Days 51
From 22-26 July 2013 there will be a Lorentz Center workshop on Arithmetic Geometry in Sage. There will be four main projects during this week.
The first project is to speed up operations with finite fields in Sage. Faster finite fields will mean that the algorithms in the other projects will also be significantly faster. According to a Google groups discussion it should be relatively easy to speed up operations in finite fields of cardinality larger than 2^16 by a factor of 10. If you are interested in working on this, please let us know.
- The second project is to enhance the function field functionality of Sage. In particular, it is important to have algorithms for computing with Jacobians of algebraic curves. It is desirable to implement two different frameworks, each with its own advantages: one developed by F. Hess and the other developed by K. Khuri-Makdisi. This project is motivated by the following two projects.
The third project is to work on practical implementations of the algorithm described in Edixhoven, Couveignes, Bosman, de Jong, and Merkl for computing Galois representations over finite fields attached to modular forms.
The fourth project is to work on computing semi-stable models of curves over local fields. The goal is a practical implementation of the algorithms that follow from the new proof of Deligne and Mumford's stable reduction theorem in: K. Arzdorf and S. Wewers, A local proof of the semistable reduction theorem, arXiv:1211.4624. This is worked out for superelliptic curves (yn = f(x) with n not divisible by the residue characteristic) by I. Bouw and S. Wewers, Computing L-functions and semistable reduction of superelliptic curves, arXiv:1211.4459.
For further information, contact one of the organizers: Peter Bruin Maarten Derickx Michiel Kosters