Limit Mordell-Weil groups and their pp-adic closure

  • Haruzo Hida

    Department of Mathematics UCLA Los Angeles, CA 90095-1555 U.S.A


This is a twin article of [H14b], where we study the projective limit of the Mordell-Weil groups (called pro Λ\Lambda-MW groups) of modular Jacobians of pp-power level. We prove a control theorem of an ind-version of the KK-rational Λ\Lambda-MW group for a number field KK. In addition, we study its pp-adic closure in the group of KpK_{\frak p}-valued points of the modular Jacobians for a p{\frak p}-adic completion KpK_{\frak p} for a prime pp\frak p|p of KK. As a consequence, if Kp=QpK_{\frak p}=\Bbb Q_p, we give an exact formula for the rank of the ordinary/co-ordinary part of the closure.