Finding large Selmer rank via an arithmetic theory of local constants

2007/09/01 by Barry Mazur, Karl Rubin · 13 citations
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Cryptography and Residue Arithmetic

paper · pdf · doi:10.4007/annals.2007.166.579

Abstract

We obtain lower bounds for Selmer ranks of elliptic curves over dihedral extensions of number fields.

Cited by

• Disparity in Selmer ranks of quadratic twists of elliptic curves
• Strong Selmer companion elliptic curves
• Twisting commutative algebraic groups
• Growth of Selmer Groups over function fields
• The Cassels-Tate pairing for finite Galois modules
• p-twisted Selmer near-companion curves
• Selmer groups of elliptic curves in degree p extensions
• A Family of Elliptic Curves with a Lower Bound on 2-Selmer Ranks of\n Quadratic Twists
• On refined conjectures of Birch and Swinnerton-Dyer type for\n Hasse-Weil-Artin L-series
• Selmer groups as flat cohomology groups
• On 2-Selmer ranks of quadratic twists of elliptic curves
• Twisting commutative algebraic groups
• On the Galois structure of Selmer groups
• The ℓ-parity conjecture over the constant quadratic extension
• Growth of Selmer rank in nonabelian extensions of number fields
• On the Iwasawa Main conjecture of abelian varieties over function fields

Related

• Finding large Selmer rank via an arithmetic theory of local constants
• On 2-Selmer ranks of quadratic twists of elliptic curves
• A heuristic for boundedness of ranks of elliptic curves
• Elliptic curves with long arithmetic progressions have large rank
• Growth of Selmer Groups over function fields