Root numbers and parity of ranks of elliptic curves

DOI10.1515/CRELLE.2011.060zbMath1314.11041arXiv0906.1815OpenAlexW1979464322MaRDI QIDQ3094344

Tim Dokchitser, Vladimir Dokchitser

Publication date: 24 October 2011

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.1815

zbMATH Keywords

elliptic curverankroot numberShafarevich-Tate conjecture

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Elliptic curves over local fields (11G07)

Related Items (18)

Invariance of the parity conjecture for $p$-Selmer groups of elliptic curves in a $D_{2p^{n}}$-extension ⋮ Introduction to the Conjectures of Birch and Swinnerton-Dyer ⋮ The \(p\)-parity conjecture for elliptic curves with a \(p\)-isogeny ⋮ The ℓ-parity conjecture over the constant quadratic extension ⋮ Multiplicities in Selmer groups and root numbers of Artin twists ⋮ Elliptic curves, \(L\)-functions, and Hilbert's tenth problem ⋮ On the parity conjecture for abelian surfaces ⋮ Brauer relations in finite groups ⋮ 2‐Selmer parity for hyperelliptic curves in quadratic extensions ⋮ Selmer ranks of quadratic twists of elliptic curves with partial rational two-torsion ⋮ The remaining cases of the Kramer–Tunnell conjecture ⋮ Root numbers and parity phenomena ⋮ GOLDFELD’S CONJECTURE AND CONGRUENCES BETWEEN HEEGNER POINTS ⋮ Variation of Tamagawa numbers of semistable abelian varieties in field extensions ⋮ Parity of ranks of elliptic curves with equivalent mod 𝑝 Galois representations ⋮ Explicit root numbers of abelian varieties ⋮ Bounds for 2-Selmer ranks in terms of seminarrow class groups ⋮ The -parity conjecture for abelian varieties over function fields of characteristic

Cites Work

• The local root number of elliptic curves with wild ramification
• Regulator constants and the parity conjecture
• On the Birch-Swinnerton-Dyer quotients modulo squares
• Ranks of twists of elliptic curves and Hilbert's tenth problem
• Local constancy in \(p\)-adic families of Galois representations
• Nonvanishing theorems for automorphic \(L\)-functions on \(\text{GL} (2)\)
• Class groups and Selmer groups
• Parity of ranks for elliptic curves with a cyclic isogeny
• Finding large Selmer rank via an arithmetic theory of local constants
• Root numbers of elliptic curves in residue characteristic 2
• Root numbers, Selmer groups, and non-commutative Iwasawa theory
• Elliptic curves with all quadratic twists of positive rank
• Self-duality of Selmer groups
• On the parity of ranks of Selmer groups IV. With an appendix by Jean-Pierre Wintenberger
• On icosahedral Artin representations, II
• REMARKS ON A CONJECTURE OF FONTAINE AND MAZUR
• Heights of Heegner points on Shimura curves.

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