On the Iwasawa invariants of elliptic curves

Abstract

Let p be an odd prime. Suppose that E is a modular elliptic curve/Q with good ordinary reduction at p. Let Q_{oo} denote the cyclotomic Z_p-extension of Q. It is conjectured that Sel_E(Q_{oo}) is a cotorsion Lambda-module and that its characteristic ideal is related to the p-adic L-function associated to E. Under certain hypotheses we prove that the validity of these conjectures is preserved by congruences between the Fourier expansions of the associated modular forms.

Abstract added in migration (taken from Greenberg's web site)

Cited by in corpus (24)

• Variation of Iwasawa invariants in Hida families
• On anticyclotomic mu-invariants of modular forms
• On the anticyclotomic Iwasawa theory of rational elliptic curves at Eisenstein primes
• Fine Selmer groups of congruent Galois representations
• Multiplicative reduction and the cyclotomic main conjecture for ${\mathrm{GL}}_2$
• Comparing anticyclotomic Selmer groups of positive coranks for congruent modular forms -- Part II
• Mazur-Tate elements of non-ordinary modular forms
• Rank parity for congruent supersingular elliptic curves
• Congruences with Eisenstein series and mu-invariants
• Root numbers and parity of local Iwasawa invariants
• Euler Characteristics and their Congruences for Multi-signed Selmer Groups
• The Manin constant in the semistable case
• Iwasawa Invariants for Symmetric Square Representations
• Fine Selmer groups of congruent $p$-adic Galois representations
• Euler Characteristics and their Congruences in the Positive Rank Setting
• Constructing Galois representations with large Iwasawa $\lambda$-Invariant
• Iwasawa Invariants for elliptic curves over ${\mathbb{Z}}_p$-extensions and Kida's Formula
• On generalized Iwasawa main conjectures and $p$-adic Stark conjectures for Artin motives
• Akashi series, characteristic elements and congruence of Galois representations
• Anticyclotomic $\mu$-invariants of residually reducible Galois Representations
• Hilbert's tenth problem in Anticyclotomic towers of number fields
• On the cohomology of plus/minus Selmer groups of supersingular elliptic curves in weakly ramified base fields
• Constructing Galois representations with prescribed Iwasawa $\lambda$-invariant
• A canonical generator for congruence ideals of Hida families