Notes on gross-zagier formula pdf

Author: kvze

August undefined, 2024

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 …

Heegner points and L-series (preliminaries)

http://davidrenshawhansen.com/gztalk.pdf 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 … margin in economics definition

Elliptic curves, L-functions, and CM-points

http://www-personal.umich.edu/~asnowden/notes/gz/L01.pdf 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 … margini niccolo falsetti

The Gross-Zagier formula: a brief introduction

Elliptic Curves and Analogies Between Number Fields and …

http://library.msri.org/books/Book49/files/07zhang.pdf http://math.columbia.edu/~goldfeld/GaussProblem.pdf margin-inline-start什么意思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 ... margin-inline-start翻译

"WebThe aim of this note is to give a survey on recent development of the Gross-Zagier formulas and their applications. The formulas relate the central derivatives (or central values) of … " - Notes on gross-zagier formula pdf

Notes on gross-zagier formula pdf

Gross{Zagier formula and arithmetic fundamental lemma

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. 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 …

Did you know?

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 … 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...

WebThis is followed by a complete proof of its coherent analogue: the Waldspurger formula, which relates the periods of integrals and the special values of L-series by means of Weil … 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 …

WebThe goal of the Gross-Zagier formula is to express L0(1;E=K) in terms of these previously de ned height functions. 5 The Gross-Zagier Formula and Applications Theorem 5.1. With all … 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 …

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-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 ... margin in ira accounthttp://library.msri.org/books/Book49/files/11ulmer.pdf cupe national rep applicationWebization [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 cup emilia romagna prenotazione