LAUSR

Abstract In this paper, we obtain bounds for the Mordell–Weil ranks over certain Z p -extensions (including cyclotomic Z p -extensions) of a wide range of abelian varieties defined over a number field F whose primes above p are totally ramified over F / Q . We assume that the abelian varieties may have good non-ordinary reduction at primes above p. Our work is a generalization of [5] , in which the second author generalized Perrin-Riou's Iwasawa theory for elliptic curves over Q with supersingular reduction ( [14] ) to elliptic curves defined over the above-mentioned number field F. As a result, we obtain bounds of the Mordell–Weil ranks over cyclotomic extensions of the Jacobian varieties of y 2 = x 3 p N + a x p N + b and y 2 p M = x 3 p N + a x p N + b .