Variation of Heegner points in Hida families

DOI10.1007/s00222-006-0007-0zbMath1171.11033arXiv1202.6358OpenAlexW3103949850MaRDI QIDQ863437

Benjamin Howard

Publication date: 26 January 2007

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.6358

zbMATH Keywords

cohomology classesEuler systembig Heegner pointsHida's universal ordinary deformationhorizontal nonvanishing conjecture

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Galois representations (11F80) Arithmetic aspects of modular and Shimura varieties (11G18) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Related Items (29)

Interpolation of generalized Heegner cycles in Coleman families ⋮ The Iwasawa main conjectures for \(\operatorname{GL}_2\) and derivatives of \(p\)-adic \(L\)-functions ⋮ Deformations of Kolyvagin systems ⋮ Big Heegner points and special values of \(L\)-series ⋮ On the nonvanishing of generalised Kato classes for elliptic curves of rank 2 ⋮ Heegner cycles and higher weight specializations of big Heegner points ⋮ \(\Lambda\)-adic families of Jacobi forms ⋮ A refined Beilinson–Bloch conjecture for motives of modular forms ⋮ An explicit comparison of anticyclotomic p-adic L-functions for Hida families ⋮ Variation of anticyclotomic Iwasawa invariants in Hida families ⋮ Anticyclotomic main conjecture and the non-triviality of Rankin-Selberg \(L\)-values in Hida families ⋮ On the elliptic Stark conjecture in higher weight ⋮ ON THE EXCEPTIONAL SPECIALIZATIONS OF BIG HEEGNER POINTS ⋮ Quaternion algebras, Heegner points and the arithmetic of Hida families ⋮ ON THE NON-TRIVIALITY OF THE -ADIC ABEL–JACOBI IMAGE OF GENERALISED HEEGNER CYCLES MODULO , II: SHIMURA CURVES ⋮ ON THE -ADIC VARIATION OF HEEGNER POINTS ⋮ Central derivatives of \(L\)-functions in Hida families ⋮ Heegner cycles and \(p\)-adic \(L\)-functions ⋮ Dihedral Iwasawa theory of nearly ordinary quaternionic automorphic forms ⋮ On Bloch-Kato Selmer groups and Iwasawa theory of \(p\)-adic Galois representations ⋮ Big Heegner points and generalized Heegner cycles ⋮ Special cohomology classes for modular Galois representations ⋮ Kolyvagin systems and Iwasawa theory of generalized Heegner cycles ⋮ Big Heegner point Kolyvagin system for a family of modular forms ⋮ On the elliptic Stark conjecture at primes of multiplicative reduction ⋮ The \(p\)-adic variation of the Gross-Kohnen-Zagier theorem ⋮ Iwasawa theory for \(\mathrm{GL}_2\times \mathrm{Res}_{K/\mathbb{Q}}\mathrm{GL}_1\) ⋮ The universal \(p\)-adic Gross-Zagier formula ⋮ Generalized Heegner cycles and p-adic L-functions in a quaternionic setting

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