Resumen de The fine Tate¿Shafarevich group

Christian Wuthrich

• Within the Tate¿Shafarevich group of an elliptic curve E defined over a number field K, there is a canonical subgroup defined by imposing stronger conditions at the places above a given prime p. This group appears naturally in the Iwasawa theory for E. We propose a study of what one can say about the relation to the full Tate¿Shafarevich group. Some numerical examples are included, as well as a few conjectures