Resumen de Special values of L-functions and false Tate curve extensions

T. Bouganis

• In this paper we show how the p-adic Rankin�Selberg product construction of Hida can be combined with freeness results of Hecke modules of Wiles to establish interesting congruences between particular special values of L-functions of elliptic curves. These congruences are part of some deep conjectural congruences that follow from the work of Kato on the non-commutative Iwasawa theory of the false Tate curve extension. In the appendix by Vladimir Dokchitser it is shown that these congruences, combined with results from Iwasawa theory for elliptic curves, give interesting results for the arithmetic of elliptic curves over non-abelian extensions.