Limit Mordell-Weil groups and their -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 -MW groups) of modular Jacobians of -power level. We prove a control theorem of an ind-version of the -rational -MW group for a number field . In addition, we study its -adic closure in the group of -valued points of the modular Jacobians for a -adic completion for a prime of . As a consequence, if , we give an exact formula for the rank of the ordinary/co-ordinary part of the closure.