The Iwasawa main conjectures for \(\operatorname{GL}_2\) and derivatives of \(p\)-adic \(L\)-functions
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Publication:2125991
DOI10.1016/j.aim.2022.108266zbMath1495.11123OpenAlexW4214488319WikidataQ123244952 ScholiaQ123244952MaRDI QIDQ2125991
Publication date: 14 April 2022
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.aim.2022.108266
Iwasawa theorySelmer groupsEuler systems\(p\)-adic \(L\)-functionsHida familiesexplicit reciprocity lawsIwasawa Main Conjecture
Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Iwasawa theory (11R23)
Related Items
Main conjectures for higher rank nearly ordinary families. I, On the Iwasawa invariants of BDP Selmer groups and BDP \(p\)-adic \(L\)-functions, Iwasawa theory for \(\mathrm{GL}_2\times \mathrm{Res}_{K/\mathbb{Q}}\mathrm{GL}_1\)
Cites Work
- Big Heegner points and special values of \(L\)-series
- On the \(p\)-converse of the Kolyvagin-Gross-Zagier theorem
- Hida families, \(p\)-adic heights, and derivatives
- Quaternion algebras, Heegner points and the arithmetic of Hida families
- Heegner cycles and \(p\)-adic \(L\)-functions
- Euler systems for Rankin-Selberg convolutions of modular forms
- \(p\)-adic \(L\)-functions for CM fields
- Variation of Heegner points in Hida families
- Anticyclotomic Iwasawa theory of CM elliptic curves
- On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer
- The Iwasawa \(\mu \)-invariant of \(p\)-adic Hecke \(L\)-functions
- Galois representations into \(\text{GL}_2(\mathbb Z_pX)\) attached to ordinary cusp forms.
- A \(p\)-adic measure attached to the zeta functions associated with two elliptic modular forms. II
- On ordinary \(\lambda\)-adic representations associated to modular forms
- The ``main conjectures of Iwasawa theory for imaginary quadratic fields
- Iwasawa theory and \(p\)-adic heights
- On the anticyclotomic main conjecture for CM fields
- The Birch and Swinnerton-Dyer formula for elliptic curves of analytic rank one
- A geometric Jacquet-Langlands correspondence for \(\mathrm{U}(2)\) Shimura varieties
- Special values of anticyclotomic \(L\)-functions.
- Iwasawa theory of Heegner points on abelian varieties of \(\text{GL}_2\) type
- Modular elliptic curves and Fermat's Last Theorem
- Nonvanishing theorems for automorphic \(L\)-functions on \(\text{GL} (2)\)
- Generalized Heegner cycles and \(p\)-adic Rankin \(L\)-series. With an appendix by Brian Conrad
- Heegner point Kolyvagin system and Iwasawa main conjecture
- On the non-vanishing of \(p\)-adic heights on CM abelian varieties, and the arithmetic of Katz \(p\)-adic \(L\)-functions
- Heegner points and Beilinson-Kato elements: a conjecture of Perrin-Riou
- Iwasawa main conjecture for Rankin-Selberg \(p\)-adic \(L\)-functions
- A proof of Perrin-Riou's Heegner point main conjecture
- Selmer groups and the indivisibility of Heegner points
- A converse to a theorem of Gross, Zagier, and Kolyvagin
- Rankin-Eisenstein classes and explicit reciprocity laws
- The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\)
- Integrality of a ratio of Petersson norms and level-lowering congruences
- Big Heegner point Kolyvagin system for a family of modular forms
- ON THE NON-TRIVIALITY OF THE -ADIC ABEL–JACOBI IMAGE OF GENERALISED HEEGNER CYCLES MODULO , II: SHIMURA CURVES
- Modules of Congruence of Hecke Algebras and L-Functions Associated with Cusp Forms
- Fonctions $L$ $p$-adiques, théorie d'Iwasawa et points de Heegner
- Height pairings in families of deformations.
- The Heegner point Kolyvagin system
- Dihedral Iwasawa theory of nearly ordinary quaternionic automorphic forms
- Euler Systems
- Hida families and p-adic triple product L-functions
- ON THE -ADIC VARIATION OF HEEGNER POINTS
- On the anticyclotomic Iwasawa main conjecture for modular forms
- Anti-cyclotomic Katz $p$-adic $L$-functions and congruence modules
- p-adic heights of Heegner points and Beilinson-Flach classes
- Anticyclotomic main conjectures for CM modular forms
- Shimura Curves and Special Values of p-adic L-functions
- On the Birch and Swinnerton-Dyer conjecture
- On the parity of ranks of Selmer groups
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