Kato's Euler system and rational points on elliptic curves. I: A \(p\)-adic Beilinson formula

DOI10.1007/s11856-013-0047-2zbMath1317.11071OpenAlexW2021817402MaRDI QIDQ2017112

Massimo Bertolini, Henri Darmon

Publication date: 25 June 2014

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11856-013-0047-2

zbMATH Keywords

special values\(p\)-adic regulatorsKato's Euler system\(K\)-theory of modular curves

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Iwasawa theory (11R23)

Related Items (17)

STARK POINTS AND -ADIC ITERATED INTEGRALS ATTACHED TO MODULAR FORMS OF WEIGHT ONE ⋮ On the regulator formulas of Bertolini, Darmon and Rotger ⋮ Elliptic curves of rank two and generalised Kato classes ⋮ Gross-Stark units and \(p\)-adic iterated integrals attached to modular forms of weight one ⋮ A numerical approach toward the \(p\)-adic Beilinson conjecture for elliptic curves over \(\mathbb{Q}\) ⋮ On \(p\)-adic \(L\)-functions for \(\text{GL}(2)\times\text{GL}(3)\) via pullbacks of Saito-Kurokawa lifts ⋮ Finite polynomial cohomology for general varieties ⋮ Stark points and the Hida-Rankin \(p\)-adic \(L\)-function ⋮ Kato's Euler system and rational points on elliptic curves. I: A \(p\)-adic Beilinson formula ⋮ Beilinson-Flach elements, Stark units and \(p\)-adic iterated integrals ⋮ Comparison between rigid and crystalline syntomic cohomology for strictly semistable log schemes with boundary ⋮ On the elliptic Stark conjecture at primes of multiplicative reduction ⋮ Heegner points and Beilinson-Kato elements: a conjecture of Perrin-Riou ⋮ Efficient Computation of Rankin p-Adic L-Functions ⋮ Beilinson-Flach elements and Euler systems I: Syntomic regulators and 𝑝-adic Rankin 𝐿-series ⋮ Toric Regulators ⋮ Exceptional zero formulae and a conjecture of Perrin-Riou

Cites Work

• Hida families and rational points on elliptic curves
• On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer
• On a class of nearly holomorphic automorhic forms
• \(p\)-adic regulators on curves and special values of \(p\)-adic \(L\)-functions
• \(p\)-adic \(L\)-functions of an elliptic curve and rational points
• Iwasawa theory of \(p\)-adic representations over a local field
• Generalized Heegner cycles and \(p\)-adic Rankin \(L\)-series. With an appendix by Brian Conrad
• Kato's Euler system and rational points on elliptic curves. I: A \(p\)-adic Beilinson formula
• Diagonal cycles and Euler systems I: A $p$-adic Gross-Zagier formula
• p-adic elliptic polylogarithm, p-adic Eisenstein series and Katz measure
• Valeur en $2$ de fonctions $L$ de formes modulaires de poids $2$ : théorème de Beilinson explicite
• The special values of the zeta functions associated with cusp forms
• Higher Regulators, Algebraic 𝐾-Theory, and Zeta Functions of Elliptic Curves
• Beilinson-Flach elements and Euler systems I: Syntomic regulators and 𝑝-adic Rankin 𝐿-series
• Syntomic regulators and \(p\)-adic integration. I: Rigid syntomic regulators
• Syntomic regulators and \(p\)-adic integration. II: \(K_2\) of curves
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