Iwasawa theory for elliptic curves

1998/09/18 by Ralph Greenberg, Greenberg, Ralph · 5 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math/9809206

openalex publication_date 1998/09/18 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We study this subject by first proving that the p-primary subgroup of the classical Selmer group for an elliptic curve with good, ordinary reduction at a prime p has a very simple and elegant description which involves just the Galois module of p-power torsion points. We then prove theorems of Mazur, Schneider, and Perrin-Riou on the basis of this description. The final section, which is half of this long paper, contains a number of results and examples including a thorough study of the mu-invariant.

Cited by

• On λ-invariants of congruent modular forms in the anticyclotomic, indefinite setting
• On the growth of Tate-Shafarevich groups of p-supersingular abelian varieties of \rm GL₂-type over ℤ_p-extensions of number fields
• On the Tamagawa number conjecture for modular forms twisted by anticyclotomic Hecke characters
• Galois cohomology of elliptic curves over anticyclotomic extensions
• On the Fitting ideals of anticyclotomic Selmer groups of elliptic curves with good ordinary reduction

Related

• The Iwasawa μ-invariants of Elliptic Curves over ℚ
• Iwasawa Theory for Elliptic Curves at Unstable Primes
• Iwasawa theory for elliptic curves at supersingular primes over Z_p-extensions of number fields
• The structure of Selmer groups and the Iwasawa main conjecture for elliptic curves
• The Iwasawa μ-invariant of certain elliptic curves of analytic rank zero