Séminaires : Séminaire Théorie des Nombres

Equipe(s) : tn,
Responsables :Ziyang Gao, Marc Hindry, Bruno Kahn, João Pedro P. dos Santos
Email des responsables : ziyang.gao@imj-prg.fr
Salle :
Adresse :



Orateur(s) Chad Schoen - ,
Titre A numerical look at the generalized Birch andSwinnerton-Dyer conjecture for certain threefolds
Horaire14:00 à 16:00
RésumeThis is joint work with JoeBuhler and Jaap Top. The generalization of the original conjecture ofBirch and Swinnerton-Dyer was formulated by Bloch and Beilinson andpredicts that the order of vanishing of the $L$-function of a threefoldat the center of the critical strip gives the rank of the Chow group ofcycles homologous to zero. We discuss an attempt to constructnull-homologous one cycles, evaluate the Abel-Jacobi map at thesecycles, and to compare the results with the apparent order of vanishingof the $L$-function.