Notes on gross-zagier formula pdf

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August undefined, 2024

WebToday we will define the objects on the two sides of the Gross–Zagier formula (one side is in terms of L-series of modular forms, the other side is in terms of Heegner points on X 0(N)). Then we can state the main theorem precisely. 1Heegner points Let x= (ϕ: E→E′) be an isogeny of elliptic curves over C, cyclic of degree N. By abuse we Webfor the entire study is a p-adic formula of Gross-Zagier type which relates the images of these diagonal cycles under the p-adic Abel-Jacobi map to special values of certain p-adic L-functions attached to the Garrett-Rankintriple convolution of three Hida families of modular forms. The main goal of this article is to describe and prove this ...

Gross{Zagier reading seminar

http://math.columbia.edu/~goldfeld/GaussProblem.pdf WebJun 21, 2005 · A new proof of Howard’s Λ-adic Gross–Zagier formula is given, via Iwasawa theory, based on the connection between Heegner points, Beilinson–Flach elements, and their explicit reciprocity laws, to the context of indefinite Shimura curves over Q attached to nonsplit quaternion algebras. 32 PDF View 2 excerpts, cites background and methods ... 1 … oramm race

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WebThe Gross–Zagier formula Vijay Srinivasan July 27, 2024 Contents 1Modular curves I 1.1The curves Y ... We note a few properties of this definition. LetC n denote a N´eron n-gon. First, … WebWe shall need the Gross–Zagier formula (see [G–Z]) (3.1) d ds L E(s)L E(s,χ d) s=1 = c E P d,P d , where P d,P d is the height pairing of a certain Heegner point P D and c E is an … WebSuch a non-critical slope result is precisely Theorem 5.1.1 (p-adic Gross-Zagier formula for non-ordinary eigenforms of arbitrary weight; which is work in progress by Kobayashi [Kob19]). More precisely, Kobayashi’s method only establishes a p-adic Gross{Zagier formula in the non-ordinary case for one of the two p-stabilization oramond temple

riemannian geometry - Gross-Zagier formulae outside of number …

Revisiting the Gross–Zagier discriminant formula Request PDF

WebWith this setup, Gross and Zagier proved: Theorem: L ′ ( E / K, 1) = h ^ ( y K) ∬ E ( C) ω ∧ i ω D, where ω is the invariant differential on E (suitably normalized), and D is the discriminant … WebIn this notes, we are trying to give an intersection formula of local heights for nonarchimedean places. It closely follows ﬁrst six sections of part III in Gross-Zagier[3]. If there is any mistake in this notes, it is due to the author’s limited ... Gross-Zagierrevisited. InHeegner points and Rankin L-series, volume49ofMath. Sci. Res. Inst ... oramond furies areaWebThis comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to ... oramm mtb race

"WebGross-Zagier-Zhang formula over function elds B: incoherent quaternion algebra over A F, i.e. division at odd number of places. B 1is division. Fix A E,!B. M U=F: Drinfeld modular curves, indexed by U ˆB . Hecke action: B acts on lim U M . A=F: abelian variety such that (up to twist by a character) ˇ A:= lim! U Hom(J(M U);A) C = JL B (˙): t ... " - Notes on gross-zagier formula pdf

Notes on gross-zagier formula pdf

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Webfollowing Zagier’s computations, we will instead consider the curve 61.a1 and do all the computations from scratch. The notes are structured around the computation of this … Webthe methods of Gross and Zagier and give a computable formula for v ‘(J(d 1;d 2)) for any pair of discriminants d 1 6= d 2 and any prime ‘ > 2. In the case that d 1 is squarefree and d 2 is the discriminant of any quadratic imaginary order, our formula can be stated in a simple closed form. We also give a conjectural closed formula when the ...

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WebGROSS-ZAGIER REVISITED BRIAN CONRAD Contents 1. Introduction 1 2. Some properties of abelian schemes and modular curves 3 3. The Serre-Tate theorem and the Grothendieck … WebDec 31, 2024 · This formula over \(\mathscr {X}\) (which is an identity of functionals on some universal ordinary automorphic representations) specialises at classical points to all the Gross–Zagier formulas ...

WebGross-Zagier formula computes L!(1,E /K) as the value of a height function. Given a ﬁnite extension k/Q,letM k be the set of all places ofk and let · v be the corresponding …

WebGross{Zagier formula is: (1) L0(E=K;1) = (easy stu ) (period) bh(y): Here the \easy stu " is made up of things like the degree of ˇ, the number of units of O K, etc.; it’s always non … Webization [Dag] of Gross’ formula for special values of L-series [Gr1]. Theorem A can be viewed as a p-adic analytic analogue of the Gross-Zagier formula, and was sug-gested by the conjectures of Mazur-Tate-Teitelbaum type formulated in [BD1], ch. 5. It is considerably simpler to prove than the Gross-Zagier formula, as it involves

Web4 DORIANGOLDFELD d,a fundamental discriminant of an imaginary quadratic ﬁeld.We shall need the Gross–Zagier formula (see [G–Z]) (3.1) d ds L E(s)L E(s,χ d) s=1 = c E P d,P d , where P d,P d is the height pairing of a certain Heegner point P D and c E is an explicit constant depending on the elliptic curve E.Gross and Zagier showed that if Eis an elliptic …

http://library.msri.org/books/Book49/files/11ulmer.pdf oramond temple tibiaWebThis general formula applies to arbitrary cuspidal automorphic representations of GL2over totally real ﬁelds holomorphic of weight 2. In this paper, over global function ﬁelds of … ip rated dado trunkingWebGross–Zagier Formula for GL(2), II SHOU-WU ZHANG Contents 1. Introduction and Notation 191 2. Automorphic Forms 195 3. Weights and Levels 197 4. Automorphic L-Series 199 5. … oramond towerWeba higher analog of the formula of Gross and Zagier (see Corollary 0.3.2 of [Z]), and applying our argument below to this situation, one gets a variant of Theorem A determining (the motive of) f by the heights of the f-components of (homologically trivial) Heegner cycles, assuming one of them has a non-trivial height. oramorph 10/5WebSep 1, 2024 · The original proof of (1.3) given by Gross and Zagier [12] relies on deep connections between the modular -invariant and elliptic curves. In recent work [21], the author of the present work... oramorph 10/5mlhttp://math.columbia.edu/~goldfeld/GaussProblem.pdf oramorph 10mg/5ml spcWebMay 11, 2016 · The Gross-Zagier formula gives something on the BSD conjecture for elliptic curves over Q. In particular the something that interest me is that if an elliptic curve as analytic rank 1, then the elliptic curve as a point of infinite order so … ip rated consumer units