49 research outputs found
CM elliptic curves of rank 2 and nonvanishing of generalised Kato classes
Let be a CM elliptic curve and a prime of good
ordinary reduction for . Assume with sign (so ) and has a rational point of infinite order. We
prove that if is -dimensional, then a certain
generalised Kato class is nonzero; and
conversely, the nonvanishing of implies that is -dimensional. For non-CM elliptic curves, a
similar result was proved in a joint work with M.-L. Hsieh. The proof in this
paper is completely different, and should extend to other settings. Moreover,
combined with work of Rubin, we can exhibit explicit bases for -dimensional
.Comment: 20 pages, comments welcom
Variation of anticyclotomic Iwasawa invariants in Hida families
Building on the construction of big Heegner points in the quaternionic
setting, and their relation to special values of Rankin-Selberg -functions,
we obtain anticyclotomic analogues of the results of Emerton-Pollack-Weston on
the variation of Iwasawa invariants in Hida families. In particular, combined
with the known cases of the anticyclotomic Iwasawa main conjecture in weight
, our results yield a proof of the main conjecture for -ordinary newforms
of higher weights and trivial nebentypus.Comment: Essentially final version, to appear in Algebra & Number Theor