Centro de Ciencias de Benasque Pedro Pascual

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Effective methods for Darmon points

2013, Aug 25 -- Aug 31

F. Fité (U. Bielefeld)
X. Guitart (U. Politècnica de Catalunya)
J.-C. Lario (U. Politècnica de Catalunya)
M. Masdeu (U. Columbia)
V. Rotger (U. Politècnica de Catalunya)

In the 90s Henri Darmon introduced the first of a series of conjectural constructions that would generalize the classical method of Heegner points to produce algebraic points on elliptic curves. Since then, many variants and generalizations have been proposed, in which the field of definition of the elliptic curve is allowed to be a number field, or the elliptic curve itself is replaced by more general modular motives. These constructions are often very explicit and even suited for algorithmic implementations, which calculate the points in concrete examples. The interest of these practical computations is at least threefold:

1. The constructions are conjectural in most of the cases; explicit computations give numerical evidence for the conjectures.
2. If the algorithm is efficient enough it can be used to finding algebraic points which would otherwise stay out of reach.
3. Some of the techniques and algorithms used in these calculations have applications beyond this one, and are of independent interest.

Several of these constructions, however, have not been yet numerically tested and the rationality conjecture is only supported by the analogy with the tested conjectures.

The aim of this workshop is to bridge the gap between theoretical constructions and explicit calculations and to foster new collaborations among the participants, in order to advance in this exciting field.


Amod Agashe
Daniel Barrera
Francesc Castella
Pierre Charollois
Henri Darmon
Lassina Dembele
Mladen Dimitrov
Francesc Fite
Xavier Guitart
Joan-Carles Lario
Alan Lauder
David Loeffler
Matteo Longo
Elisa Lorenzo
Marc Masdeu
Juan Restrepo
Victor Rotger
Mehmet Haluk Sengun
Marco Seveso
Mak Trifkovic
Rodolfo Venerucci
Carlos de Vera
Chris Williams
Sarah Zerbes

Further Information.

This session has received financial support from the following institutions:

  • logo CSIC
  • Ministerio de educación y ciencia
  • Ayuntamiento de Benasque
  • Gobierno de Aragón
  • Universidad de Zaragoza


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