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Títol:	Ribet Bimodules and the Specialization of Heegner points
Autor/a:	Molina Blanco, Santiago
Abstract:	For a given order R in an imaginary quadratic field K, we study the specialization of the set CM(R) of Heegner points on the Shimura curve X = X0(D,N) at primes p | DN. As we show, if p does not divide the conductor of R, a point P in CM(R) specializes to a singular point (resp. a connected component) of the special fiber Xp of X at p if p ramifies (resp. does not ramify) in K. Exploiting the moduli interpretation of X0(D,N) and K. Ribet’s theory of bimodules, we give a construction of a correspondence between CM(R) and a set of conjugacy classes of optimal embeddings of R into a suitable order in a definite quaternion algebras that allows the explicit computation of these specialization maps. This correspondence intertwines the natural actions of Pic(R) and of an Atkin-Lehner group on both sides. As a consequence of this and the work of P. Michel, we derive a result of equidistribution of Heegner points in Xp. We also illustrate our results with an explicit example.
Matèries:	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra -Algebra -Shimura varieties -Curves, Elliptic -Arithmetical -Aritmètica -Varietats de Shimura -Corbes modulars -Àlgebra
Drets:	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Tipus de document:	Article - Versió publicada Article
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