Geodesic
Limit Mordell-Weil groups and their $p$-adic closure
Documenta mathematica, Alexander S. Merkurjev's Sixtieth Birthday (2015), pp. 221-264.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

This is a twin article of [H14b], where we study the projective limit of the Mordell-Weil groups (called pro $\Lambda$-MW groups) of modular Jacobians of $p$-power level. We prove a control theorem of an ind-version of the $K$-rational $\Lambda$-MW group for a number field $K$. In addition, we study its $p$-adic closure in the group of $K_{\frak p}$-valued points of the modular Jacobians for a ${\frak p}$-adic completion $K_{\frak p}$ for a prime $\frak p|p$ of $K$. As a consequence, if $K_{\frak p}=\Bbb Q_p$, we give an exact formula for the rank of the ordinary/co-ordinary part of the closure.
Classification : 11F25, 11F32, 11D45, 11G05, 11G10, 11G18, 14H40
Keywords: modular curve, Hecke algebra, modular deformation, analytic family of modular forms, Mordell-Weil group, modular Jacobian 
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Hida, Haruzo. Limit Mordell-Weil groups and their $p$-adic closure. Documenta mathematica, Alexander S. Merkurjev's Sixtieth Birthday (2015), pp. 221-264. http://geodesic.mathdoc.fr/item/DOCMA_2015__S2__a15/