Vanishing of L-functions and ranks of Selmer groups

• Autores: Christopher Skinner, Eric Urban
• Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé, Javier Soria de Diego, Juan Luis Varona Malumbres, Joan Verdera, Vol. 2, 2006, ISBN 978-3-03719-022-7, págs. 473-500
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • This paper connects the vanishing at the central critical value of the L-functions of certain polarized regular motives with the positivity of the rank of the associated p-adic (Bloch�Kato) Selmer groups. For the motives studied it is shown that vanishing of the Lvalue implies positivity of the rank of the Selmer group. It is further shown that if the order of vanishing is positive and even then the Selmer group has rank at least two. The proofs make extensive use of families of p-adic modular forms. Additionally, the proofs assume the existence of Galois representations associated to holomorphic eigenforms on unitary groups over an imaginary quadratic field.