A Conjectural Extension of the Gross-Zagier Formula on Singular Moduli
نویسندگان
چکیده
منابع مشابه
The Gross-zagier Formula on Singular Moduli for Shimura Curves
The Gross-Zagier formula on singular moduli can be seen as a calculation of the intersection multiplicity of two CM divisors on the integral model of a modular curve. We prove a generalization of this result to a Shimura curve.
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The famous results of Gross and Zagier compare the heights of Heegner points on modular curves with special values of the derivatives of related L-functions. When specialized to the level 1 case (i.e., the full modular curve H/Γ, where Γ = SL2(Z)), we recover an astounding formula for the differences of singular moduli (the Heegner points on the full modular curve) in terms of an explicit prime...
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act on the upper half-plane by linear fractional transformations. We may form the quotient Y0(N) = Γ0(N)\H, a Riemann surface with finitely many cusps. Compactifying gives a curve X0(N) which is in fact defined over Q; the map z → (j(z), j(Nz)) ∈ AC realizes Y0(N) as a (highly singular) plane curve with Q-coefficients. Over a general field k of characteristic zero, the k-points of the curve X0(...
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These are the notes of a talk given by Prof. Dick Gross. The talk was the first one of a graduate student seminar held at Harvard, Fall 2013, and was aimed at providing an introduction to the Gross-Zagier formula and related things from an expert’s perspective. The notes were taken by Yihang Zhu, and he is respondible for any mistakes or inaccuracies. Please contact him at [email protected]...
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The recent work [YZZ] completes a general Gross–Zagier formula for Shimura curves. Meanwhile an arithmetic version of Gan–Gross–Prasad conjecture proposes a vast generalization to higher dimensional Shimura varieties. We will discuss the arithmetic fundamental lemma arising from the author’s approach using relative trace formulae to this conjecture.
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ژورنال
عنوان ژورنال: Tokyo Journal of Mathematics
سال: 1998
ISSN: 0387-3870
DOI: 10.3836/tjm/1270042000