ON THE EXCEPTIONAL SPECIALIZATIONS OF BIG HEEGNER POINTS

DOI10.1017/S1474748015000444zbMath1390.11094OpenAlexW2963636478MaRDI QIDQ4600334

Francesc Castella

Publication date: 8 January 2018

Published in: Journal of the Institute of Mathematics of Jussieu (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1474748015000444

zbMATH Keywords

\(p\)-adic \(L\)-functions\(L\)-invariantsderivative formulaHida familiesGross-Zagier formulaHeegner poihts

Mathematics Subject Classification ID

Elliptic curves (14H52) Complex multiplication and moduli of abelian varieties (11G15) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Varieties over global fields (11G35)

Related Items

Generalized Kato classes and exceptional zero conjectures ⋮ On the elliptic Stark conjecture in higher weight ⋮ ON THE -ADIC VARIATION OF HEEGNER POINTS ⋮ The exceptional zero phenomenon for elliptic units ⋮ On the elliptic Stark conjecture at primes of multiplicative reduction ⋮ Anticyclotomic 𝑝-adic 𝐿-functions and the exceptional zero phenomenon ⋮ Heegner points and Beilinson-Kato elements: a conjecture of Perrin-Riou ⋮ On the \(p\)-adic Birch and Swinnerton-Dyer conjecture for elliptic curves over number fields

Cites Work

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• Exceptional zero formulae and a conjecture of Perrin-Riou
• Euler systems for Rankin-Selberg convolutions of modular forms
• Variation of Heegner points in Hida families
• On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer
• Galois representations into \(\text{GL}_2(\mathbb Z_pX)\) attached to ordinary cusp forms.
• On ordinary \(\lambda\)-adic representations associated to modular forms
• On the behavior of \(p\)-adic \(L\)-functions at \(s=0\)
• Gauss sums and the p-adic \(\Gamma\)-function
• Derivatives of \(p\)-adic \(L\)-functions, Heegner cycles and monodromy modules attached to modular forms
• Ordinary \(p\)-adic étale cohomology groups attached to towers of elliptic modular curves. II
• Generalized Heegner cycles and \(p\)-adic Rankin \(L\)-series. With an appendix by Brian Conrad
• Rankin-Eisenstein classes and explicit reciprocity laws
• \(p\)-adic \(L\)-functions and \(p\)-adic periods of modular forms
• Heegner cycles and higher weight specializations of big Heegner points
• Central derivatives of \(L\)-functions in Hida families
• A generalization of the Coleman map for Hida deformations
• On the p-adic Eichler-Shimura isomorphism for Λ-adic cusp forms.
• Euler Systems
• ON THE -ADIC VARIATION OF HEEGNER POINTS
• On the parity of ranks of Selmer groups
• Classical and overconvergent modular forms