The -adic Gross–Zagier formula on Shimura curves

DOI10.1112/S0010437X17007308zbMath1392.11042arXiv1510.02114MaRDI QIDQ5369308

Daniel Disegni

Publication date: 16 October 2017

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.02114

zbMATH Keywords

Heegner pointsBirch and Swinnerton-Dyer conjectureGross-Zagier formulap-adic L-functionp-adic heights

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Related Items (16)

p-adic L-functions via local–global interpolation: the case of ⋮ Heegner cycles and congruences between anticyclotomic \(p\)-adic \(L\)-functions over CM-extensions ⋮ The congruent number problem and elliptic curves ⋮ THE p-ADIC GROSS–ZAGIER FORMULA ON SHIMURA CURVES, II: NONSPLIT PRIMES ⋮ A \(p\)-adic arithmetic inner product formula ⋮ Local Langlands correspondence, local factors, and zeta integrals in analytic families ⋮ Anticyclotomic \(p\)-adic \(L\)-functions for elliptic curves at some additive reduction primes ⋮ Big Heegner points and generalized Heegner cycles ⋮ -adic -functions for ⋮ On the non-vanishing of \(p\)-adic heights on CM abelian varieties, and the arithmetic of Katz \(p\)-adic \(L\)-functions ⋮ Beilinson-Kato and Beilinson-Flach elements, Coleman-Rubin-Stark classes, Heegner points and a conjecture of Perrin-riou ⋮ \(p\)-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin ⋮ Functoriality of automorphic \(L\)-invariants and applications ⋮ On the \(p\)-adic Birch and Swinnerton-Dyer conjecture for elliptic curves over number fields ⋮ \(p^{\infty}\)-Selmer groups and rational points on CM elliptic curves ⋮ The universal \(p\)-adic Gross-Zagier formula

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