Growth of Selmer rank in nonabelian extensions of number fields

DOI10.1215/00127094-2008-025zbMath1151.11023arXivmath/0703363OpenAlexW2127639879MaRDI QIDQ935194

Barry Mazur, Karl Rubin

Publication date: 5 August 2008

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703363

zbMATH Keywords

elliptic curvesMordell-Weil rankSelmer groupsparity conjectureHilbert class field towers

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Rational points (14G05) Elliptic curves over global fields (11G05) Iwasawa theory (11R23)

Related Items

Compatibility of arithmetic and algebraic local constants (the case ) ⋮ Regulator constants and the parity conjecture ⋮ Rank growth of elliptic curves over 𝑁-th root extensions ⋮ Ankeny-Artin-Chowla and Mordell conjectures in terms of \(p\)-rationality ⋮ The work of Barry Mazur ⋮ Iwasawa Theory, projective modules, and modular representations ⋮ Root numbers, Selmer groups, and non-commutative Iwasawa theory ⋮ THE GROWTH OF THE SELMER GROUP OF AN ELLIPTIC CURVE WITH SPLIT MULTIPLICATIVE REDUCTION ⋮ On the parity of ranks of Selmer groups IV. With an appendix by Jean-Pierre Wintenberger

Uses Software

• ecdata

Cites Work

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• On the Birch-Swinnerton-Dyer quotients modulo squares
• Systematic growth of Mordell-Weil groups of abelian varieties in towers of number fields
• Generalizing the Birch-Stephens theorem. I: Modular curves
• Finding large Selmer rank via an arithmetic theory of local constants
• \(p\)-adic analytic groups
• On the parity of ranks of Selmer groups II
• The parity conjecture for elliptic curves at supersingular reduction primes
• Scarcity and abundance of trivial zeros in division towers
• Root numbers, Selmer groups, and non-commutative Iwasawa theory
• Infinite class field towers of quadratic fields.
• Twisted Hasse-Weil L-Functions and the Rank of Mordell-Weil Groups