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## Sage Days: Algorithms in Arithmetic Geometry |

From
22-26 July 2013 there will be a Lorentz Center workshop on Arithmetic Geometry
in Sage. There will be three main projects during this week. - 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 second
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 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 (in preparation).
- 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 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.
For
further information, contact one of the organizers: Peter Bruin Maarten Derickx
Michiel Kosters [Back] |