Notes on gross-zagier formula pdf

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August undefined, 2024

WebThe purpose of this paper is to discuss some work on elliptic curves over function ﬁelds inspired by the Gross–Zagier theorem and to present new ideas about ranks of elliptic curves from the function ﬁeld case which I hope will inspire work over number ﬁelds. 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 ...

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WebNov 20, 2024 · The theorems of Gross–Zagier and Zhang relate the Néron–Tate heights of complex ... Zhang, S.-W., Gross-Zagier formula for GL(2). II. In: Heegner Points and Rankin … 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 … razor shark free to play

DIAGONAL CYCLES AND EULER SYSTEMS I: A p-ADIC GROSS …

WebSep 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... 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 … 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 … simpsonville walmart hours

A FRIENDLY INTRODUCTION TO THE RESULTS OF …

[PDF] The universal p-adic Gross–Zagier formula - Semantic Scholar

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 … WebGROSS-ZAGIER FORMULA NOTES TAKEN BY MIKE WOODBURY These are notes taken in Tonghai Yang’s course titled “The Gross-Zagier For-mula” at the University of Wisconsin … simpsonville wells fargohttp://davidrenshawhansen.com/gztalk.pdf simpsonville waste and recycling

"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 ... " - Notes on gross-zagier formula pdf

Notes on gross-zagier formula pdf

[PDF] The Iwasawa theoretic Gross–Zagier theorem - Semantic …

Web1. AN OVERVIEW OF THE GROSS-ZAGIER AND WALDSPURGER FORMULAS (YUNQING TANG)9 The theory of complex multiplication implies that Heegner points are deﬁned … WebDec 31, 2024 · David Loeffler, R. Rockwood, Sarah Livia Zerbes. Mathematics. 2024. We prove a “twist-compatibility” result for p-adic families of cohomology classes associated to symmetric spaces. This shows that a single family of classes (lying in a finitely-generated Iwasawa…. Expand.

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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 ... Webon Gross{Zagier formula ([YZZ]) which serves as a prototype of the more gen-eral arithmetic restriction problems (stated in e.g., [Zh4]). We then present the relative trace formula …

http://library.msri.org/books/Book49/files/11ulmer.pdf WebThis 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 …

http://www-personal.umich.edu/~asnowden/notes/gz/L01.pdf Webtion formula. Theorem A. For any unramiﬁed cuspidal automorphic representation π, and for any even r≥0, h[Shtr T1] π,[Sht r T2] i= Cr(π). Theorem A is the function ﬁeld analogue of the Gross-Kohnen-Zagier formula [5, Theorem B], but for higher order derivatives. The original Gross-Kohnen-Zagier formula corresponds to the case r= 1 over ...

Weba 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.

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-Rankin triple convolution of three Hida families of modular forms. The main goal of this article is to describe and prove this ... razor shark gratis spielenWeb2 Gross-Zagier Subgroups In this section, we x our notation and conventions, and de ne the Manin constant. Then we recall the statement of the full Birch and Swinnerton-Dyer conjecture over an imaginary quadratic eld K. We give a new de nition of Gross-Zagier subgroups of E(K) and prove that they all satisfy a Gross-Zagier style formula. When r ... razor shark hackWebThis comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to ... simpson viper helmet tear offsWebSuch 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 razor shark free spinsWebGross-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 … simpsonville water park schttp://library.msri.org/books/Book49/files/07zhang.pdf simpsonville wrecker serviceWebWe 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 … simpsonvill sc kidnappers news