Parity of ranks of elliptic curves with equivalent mod 𝑝 Galois representations

DOI10.1090/proc/12993zbMath1346.14086OpenAlexW2338370800MaRDI QIDQ2809181

Sudhanshu Shekhar

Publication date: 27 May 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/12993

zbMATH Keywords

elliptic curvescongruencesIwasawa theorySelmer groups\(\text{mod\,}p\) Galois representations

Mathematics Subject Classification ID

Elliptic curves (14H52) Congruences for modular and (p)-adic modular forms (11F33) Iwasawa theory (11R23)

Related Items (5)

Multiplicities in Selmer groups and root numbers of Artin twists ⋮ \(\lambda\)-invariant stability in families of modular Galois representations ⋮ Root numbers and parity of local Iwasawa invariants ⋮ On the signed Selmer groups of congruent elliptic curves with semistable reduction at all primes above $p$ ⋮ Rank parity for congruent supersingular elliptic curves

Cites Work

• Variation of Iwasawa invariants in Hida families
• Completely faithful Selmer groups over Kummer extensions
• On the Iwasawa invariants of elliptic curves
• Finite submodules and Iwasawa \(\mu\)-invariants
• Modular elliptic curves and Fermat's Last Theorem
• On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
• Root numbers and parity of ranks of elliptic curves
• Computations in non-commutative Iwasawa theory
• On the structure of Selmer groups over 𝑝-adic Lie extensions
• Euler characteristics and elliptic curves. II.
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