On Shafarevich-Tate groups and analytic ranks in families of modular forms. I: Hida families

DOI10.2422/2036-2145.202206_011MaRDI QIDQ6638222

Publication date: 14 November 2024

Published in: Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V (Search for Journal in Brave)

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Algebraic cycles (14C25)

Cites Work

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On the $p$-converse of the Kolyvagin-Gross-Zagier theorem
On Zagier's conjecture for base changes of elliptic curves
Quaternion algebras, Heegner points and the arithmetic of Hida families
On the critical values of Hecke $L$-functions for imaginary quadratic fields
Kolyvagin's method for Chow groups and Kuga-Sato varieties
Variation of Iwasawa invariants in Hida families
Variation of Heegner points in Hida families
Hida families and rational points on elliptic curves
On $p$-adic analogues of the conjectures of Birch and Swinnerton-Dyer
On $L$-functions of elliptic curves and cyclotomic towers
On $L$-functions of elliptic curves and anticyclotomic towers
A p-adic measure attached to the zeta functions associated with two elliptic modular forms. I
Height pairings for algebraic cycles
Heegner points and derivatives of $L$-series
Galois representations into $\text{GL}_2(\mathbb Z_p X)$ attached to ordinary cusp forms.
L-functions and division towers
On ordinary $\lambda$-adic representations associated to modular forms
Twists of modular forms and endomorphisms of abelian varieties
Galois representations, Kähler differentials and ``main conjectures
Arithmetic intersection theory
Mean values of derivatives of modular $L$-series
Endomorphisms of semi-stable Abelian varieties over number fields
Relations between $K_2$ and Galois cohomology
Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
On the image of $p$-adic regulators
Modular forms and $p$-adic Hodge theory
Heights of Heegner cycles and derivatives of L-series
On the image of $\Lambda$-adic Galois representations
Variation of anticyclotomic Iwasawa invariants in Hida families
Motives for modular forms
On the $p$-adic height of Heegner cycles
Generalized Heegner cycles and $p$-adic Rankin $L$-series. With an appendix by Brian Conrad
On Bloch-Kato Selmer groups and Iwasawa theory of $p$-adic Galois representations
Big Heegner points and generalized Heegner cycles
The Iwasawa main conjectures for $\operatorname{GL}_2$ and derivatives of $p$-adic $L$-functions
Selmer groups and the indivisibility of Heegner points
Kolyvagin systems and Iwasawa theory of generalized Heegner cycles
Gross-Kohnen-Zagier theorem for higher weight forms
A converse to a theorem of Gross, Zagier, and Kolyvagin
Rankin-Eisenstein classes and explicit reciprocity laws
$p$-adic $L$-functions and $p$-adic periods of modular forms
The rationality of Stark-Heegner points over genus fields of real quadratic fields
The Iwasawa Main Conjectures for $\mathrm{GL}_{2}$
Central derivatives of $L$-functions in Hida families
Nonvanishing theorems for L-functions of modular forms and their derivatives
A NOTE ON CONTROL THEOREMS FOR QUATERNIONIC HIDA FAMILIES OF MODULAR FORMS
On the local divisibility of Heegner points
Congruences Between Systems of Eigenvalues of Modular Forms
A generalisation of the Cassel-Tate pairing.
On the Zero Locus of Normal Functions and the Etale Abel-Jacobi Map
on l-adic representations attached to modular forms II
Iwasawa modules attached to congruences of cusp forms
Formes modulaires de poids $1$
Sur les représentations $l$-adiques associées aux formes modulaires de Hilbert
Dihedral Iwasawa theory of nearly ordinary quaternionic automorphic forms
ON THE -ADIC VARIATION OF HEEGNER POINTS
Vanishing of special values and central derivatives in Hida families
A refined Beilinson–Bloch conjecture for motives of modular forms
On the structure of Selmer and Shafarevich–Tate groups of even weight modular forms
Locally Indecomposable Galois Representations
On the Birch and Swinnerton-Dyer conjecture
On the parity of ranks of Selmer groups

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