Iwasawa theory of Heegner points on abelian varieties of \(\text{GL}_2\) type

DOI10.1215/S0012-7094-04-12411-XzbMath1068.11071arXiv1202.6342OpenAlexW2074338473MaRDI QIDQ1880377

Benjamin Howard

Publication date: 27 September 2004

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

Full work available at URL: https://arxiv.org/abs/1202.6342

zbMATH Keywords

Heegner pointsHilbert modular form

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Abelian varieties of dimension (> 1) (11G10) Iwasawa theory (11R23)

Related Items

The Iwasawa main conjectures for \(\operatorname{GL}_2\) and derivatives of \(p\)-adic \(L\)-functions, ON THE QUATERNIONIC p-ADIC L-FUNCTIONS ASSOCIATED TO HILBERT MODULAR EIGENFORMS, Variation of Heegner points in Hida families, The vanishing of anticyclotomic \(\mu\)-invariants for non-ordinary modular forms, On the BDP Iwasawa main conjecture for modular forms, Some remarks on the two-variable Main Conjecture of Iwasawa theory for elliptic curves without complex multiplication, On the Iwasawa invariants of BDP Selmer groups and BDP \(p\)-adic \(L\)-functions, On the Bloch-Kato conjecture for Hilbert modular forms, A proof of Perrin-Riou's Heegner point main conjecture, Heegner point Kolyvagin system and Iwasawa main conjecture, Exceptional zero formulae for anticyclotomic \(p\)-adic \(L\)-functions of elliptic curves in the ramified case, Dihedral Iwasawa theory of nearly ordinary quaternionic automorphic forms, Kolyvagin systems and Iwasawa theory of generalized Heegner cycles, Beilinson-Kato and Beilinson-Flach elements, Coleman-Rubin-Stark classes, Heegner points and a conjecture of Perrin-riou, The symmetric structure of the plus/minus Selmer groups of elliptic curves over totally real fields and the parity conjecture, On the anticyclotomic Iwasawa theory of rational elliptic curves at Eisenstein primes, On anticyclotomic variants of the \(p\)-adic Birch and Swinnerton-Dyer conjecture, Bipartite Euler systems, On the anticyclotomic Iwasawa theory of CM forms at supersingular primes

Cites Work

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• Arithmétique des algèbres de quaternions
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• Mazur's conjecture on higher Heegner points.
• Special values of anticyclotomic \(L\)-functions.
• Kummer theory for abelian varieties over local fields
• Construction of class fields and zeta functions of algebraic curves
• On the parity of ranks of Selmer groups II
• A generalisation of the Cassel-Tate pairing.
• Galois Action on Division Points of Abelian Varieties with Real Multiplications
• Kolyvagin systems
• Heights of Heegner points on Shimura curves.