General Selmer groups and critical values of Hecke \(L\)-functions
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Publication:1318161
DOI10.1007/BF01459498zbMath0789.14018OpenAlexW1998149513MaRDI QIDQ1318161
Publication date: 16 June 1994
Published in: Mathematische Annalen (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/165128
elliptic curveSelmer groupscomplex multiplicationTate-Shafarevich groupHecke \(L\)-functionsBirch and Swinnerton-Dyer conjectureGrössencharacter
Rational points (14G05) Arithmetic ground fields for curves (14H25) Elliptic curves (14H52) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Complex multiplication and abelian varieties (14K22) Global ground fields in algebraic geometry (14G25)
Related Items
Regulator constants and the parity conjecture ⋮ A deformation problem for Galois representations over imaginary quadratic fields ⋮ Estimating the growth in Mordell-Weil ranks and Shafarevich-Tate groups over Lie extensions ⋮ Nonvanishing of Hecke \(L\)-functions and the Bloch-Kato conjecture ⋮ Congruences between Selmer groups ⋮ Iwasawa Theory, projective modules, and modular representations ⋮ Root numbers, Selmer groups, and non-commutative Iwasawa theory ⋮ The Tamagawa number conjecture of adjoint motives of modular forms ⋮ On the Birch-Swinnerton-Dyer quotients modulo squares ⋮ Self-duality of Selmer groups ⋮ On the Eisenstein ideal for imaginary quadratic fields
Cites Work
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- \(p\)-adic \(L\)-functions for CM fields
- L-functions and division towers
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- The ``main conjectures of Iwasawa theory for imaginary quadratic fields
- Rational points of Abelian varieties with values in towers of number fields
- Arithmétique des courbes elliptiques et théorie d'Iwasawa
- On the Birch and Swinnerton-Dyer conjecture
- On the critical values of Hecke L-series
