The Gross-Zagier Formula on Shimura Curves

From MaRDI portal
Publication:4899817

DOI10.1515/9781400845644zbMath1272.11082OpenAlexW4302468743MaRDI QIDQ4899817

Xinyi Yuan, Wei Zhang, Shou-Wu Zhang

Publication date: 10 January 2013

Full work available at URL: https://doi.org/10.1515/9781400845644




Related Items (67)

Quadratic Twists of Elliptic CurvesThe Birch and Swinnerton-Dyer Conjecture: A brief surveyAverage CM-values of higher Green's function and factorizationSTARK POINTS AND -ADIC ITERATED INTEGRALS ATTACHED TO MODULAR FORMS OF WEIGHT ONETHE IWASAWA MAIN CONJECTURE FOR HILBERT MODULAR FORMSCuspidal part of an Eisenstein series restricted to an index 2 subfieldAn intersection formula for CM cycles on Lubin-Tate spacesBase change and triple product 𝐿-seriesWaldspurger formula over function fieldsConstruction of anti-cyclotomic Euler systems of modular abelian varieties, and the ranks of their Mordell-Weil groupsThe Gross-Zagier-Zhang formula over function fieldsCube sums of the forms \(3p\) and \(3p^2\)Shtukas and the Taylor expansion of \(L\)-functionsA \(p\)-adic Waldspurger formulap-adic L-functions via local–global interpolation: the case ofShimura curves and the abc conjectureOn the global Gan-Gross-Prasad conjecture for general spin groupsOn Heegner points for primes of additive reduction ramifying in the base fieldThe congruent number problem and elliptic curvesPlectic Stark-Heegner pointsOn arithmetic fundamental lemmasTHE p-ADIC GROSS–ZAGIER FORMULA ON SHIMURA CURVES, II: NONSPLIT PRIMESFaltings heights of abelian varieties with complex multiplicationOn the averaged Colmez conjectureHeegner points and the arithmetic of elliptic curves over ring class extensionsA \(p\)-adic Waldspurger formula and the conjecture of Birch and Swinnerton-DyerA \(p\)-adic arithmetic inner product formulaOn the Northcott property for special values of \(L\)-functionsHeegner points on modular curvesCube sums of the forms \(3p\) and \(3p^2\). IICentral values of \(L\)-functions of cubic twistsThe -adic Gross–Zagier formula on Shimura curvesFirst moment of Rankin-Selberg central \(L\)-values and subconvexity in the level aspectON THE NON-TRIVIALITY OF THE -ADIC ABEL–JACOBI IMAGE OF GENERALISED HEEGNER CYCLES MODULO , II: SHIMURA CURVESArithmetic diagonal cycles on unitary Shimura varietiesArithmetic theta lifts and the arithmetic Gan-Gross-Prasad conjecture for unitary groupsFourier transform and the global Gan-Gross-Prasad conjecture for unitary groups2-Selmer groups, 2-class groups and rational points on elliptic curvesAUTOMORPHIC SL 2 ‐PERIODS AND THE SUBCONVEXITY PROBLEM FOR GL 2 × GL 3On the Bloch-Kato conjecture for Hilbert modular formsA summation formula for triples of quadratic spacesCongruent numbersRecent progress on the Gross-Prasad conjectureAn automorphic approach to Darmon pointsThe even parity Goldfeld conjecture: congruent number elliptic curvesAutomorphic period and the central value of Rankin-Selberg L-functionCM cycles on Kuga-Sato varieties over Shimura curves and Selmer groupsA proof of Perrin-Riou's Heegner point main conjectureArithmetic intersection on GSpin Rapoport–Zink spaces\(p\)-adic interpolation of automorphic periods for GL\(_2\)Anticyclotomic \(p\)-adic \(L\)-functions for elliptic curves at some additive reduction primesExceptional zero formulae for anticyclotomic \(p\)-adic \(L\)-functions of elliptic curves in the ramified casePoints of order 13 on elliptic curvesQuadratic twists of elliptic curvesLinear forms, algebraic cycles, and derivatives of \(L\)-seriesOn the non-vanishing of \(p\)-adic heights on CM abelian varieties, and the arithmetic of Katz \(p\)-adic \(L\)-functionsBeilinson-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 RubinChow groups and \(L\)-derivatives of automorphic motives for unitary groupsAnticyclotomic 𝑝-adic 𝐿-functions and the exceptional zero phenomenonAn explicit Gross–Zagier formula related to the Sylvester conjectureOn the \(p\)-adic Birch and Swinnerton-Dyer conjecture for elliptic curves over number fields\(p^{\infty}\)-Selmer groups and rational points on CM elliptic curvesThe universal \(p\)-adic Gross-Zagier formulaPullbacks of Saito-Kurokawa lifts and a central value formula for degree 6 \(L\)-seriesOn the $8$ case of the Sylvester conjectureKudla–Rapoport cycles and derivatives of local densities




This page was built for publication: The Gross-Zagier Formula on Shimura Curves