Iwasawa theory for elliptic curves at supersingular primes over Z_p-extensions of number fields

2004/11/22 by Adrian Iovita, Iovita, Adrian, Robert Pollack +1 · 1 citation
Mathematics · #11G05 #11R23 #11S31 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G05 #msc:11R23 #msc:11S31

paper · pdf · doi:10.48550/arxiv.math/0411496

35 pages

arxiv created 2004/11/22 · arxiv updated 2009/12/01

Abstract

In this paper, we make a study of the Iwasawa theory of an elliptic curve at a supersingular prime p along an arbitrary Z_p-extension of a number field K in the case when p splits completely in K. Generalizing work of Kobayashi and Perrin-Riou, we define restricted Selmer groups and λ^±, μ^±-invariants; we then derive asymptotic formulas describing the growth of the Selmer group in terms of these invariants. To be able to work with non-cyclotomic Z_p-extensions, a new local result is proven that gives a complete description of the formal group of an elliptic curve at a supersingular prime along any ramified Z_p-extension of Q_p.

Cited by

• On the growth of Tate-Shafarevich groups of p-supersingular abelian varieties of \rm GL₂-type over ℤ_p-extensions of number fields

Related

• Plus/minus Heegner points and Iwasawa theory of elliptic curves at\n supersingular primes
• Iwasawa theory for elliptic curves at supersingular primes: A pair of\n main conjectures
• On the growth of μ-invariant in Iwasawa theory of supersingular Elliptic curves
• Residual Supersingular Iwasawa Theory over quadratic imaginary fields
• Anticyclotomic Iwasawa theory of abelian varieties of GL₂-type at non-ordinary primes