On the averaged colmez conjecture

Author: zxfj

August undefined, 2024

Web17 de dez. de 2024 · This is an expository article on the averaged version of Colmez’s conjecture, relating Faltings heights of CM abelian varieties to Artin $L$-functions. It is … Web1 de abr. de 2010 · Abstract In this paper, we reinterpret the Colmez conjecture on the Faltings height of $\text{CM}$ abelian varieties in terms of Hilbert (and Siegel) modular forms. We construct an elliptic modular form involving the Faltings height of a $\text{CM}$ abelian surface and arithmetic intersection numbers, and prove that the Colmez …

On the averaged Colmez conjecture — Princeton University

WebThe Colmez conjecture, proposed by Colmez, is a conjecture expressing the Faltings height of a CM abelian variety in terms of some linear combination of logarithmic … Web1 de nov. de 2024 · Abstract: This is an expository article on the averaged version of Colmez's conjecture, relating Faltings heights of CM abelian varieties to Artin L … rcv depreciation and acv

Xinyi Yuan* [email protected]), Berkeley, CA 94702. On the …

WebFirst let us recall the definition of Faltings heights introduced by Faltings . Let A𝐴Aitalic_A be an abelian variety of dimension g𝑔gitalic_g over a number field K𝐾Kital Web24 de jul. de 2015 · Abstract: The Colmez conjecture, proposed by Colmez, is a conjecture expressing the Faltings height of a CM abelian variety in terms of some linear … WebAbstract. We give a proof of the André-Oort conjecture for A g — the moduli space of principally polarized abelian varieties. In particular, we show that a recently proven “averaged” version of the Colmez conjecture yields lower bounds for Galois orbits of CM points. The André-Oort conjecture then follows from previous work of Pila and ... rcvd hypoallergenic

La Rha C Torique Dans L Antiquita C (book)

[1507.06903v3] On the Averaged Colmez Conjecture

WebWhen d=2, Yang [Yan13] was able to prove Colmez’s conjecture in many cases, including the rst known cases of non-abelian extensions. Our rst main result, stated in the text as Theorem 9.5.5, is the proof of an averaged form of Colmez’s conjecture for a xed E, obtained by averaging both sides of the conjectural formula over all CM types. Web21 de dez. de 2015 · The Colmez conjecture is a formula expressing the Faltings height of an abelian variety with complex multiplication in terms of some linear combination of … rcvd glycobalanceWeb24 de jul. de 2015 · PDF The Colmez conjecture, proposed by Colmez, ... On the Averaged Colmez Conjecture. Xinyi Y uan and Shou-Wu Zhang. July 27, 2015. … simulate mouse wheel on laptop

"WebUsing this, the averaged Colmez conjecture for E can be reduced to the exact Colmez conjecture for (E♯,Φ♯). Admittedly, at the moment this looks less like a reduction and … " - On the averaged colmez conjecture

On the averaged colmez conjecture

$arXiv:1811.00428v2 [math.NT] 4 Dec 2024$

Web6 de dez. de 2024 · Speaker: Roy Zhao (University of California Berkeley) Title: Heights on quaternionic Shimura varieties Abstract: We give an explicit formula for the height of a special point on a quaternionic Shimura variety in terms of Faltings heights of CM abelian varieties. This is a generalization of the work of Yuan and Zhang on proving the … Web1.J. Tsimerman A proof of the Andre-Oort conjecture for A g, arXiv:1506.01466 [math.NT]. 2.X. Yuan and S. Zhang On the Averaged Colmez Conjecture, arXiv:1507.06903 [math.NT]. Two previous lectures 1.S. Zhang, Equidistributions for torsion points and small points, AG’95, Santa Cruz 2.S. Zhang, Heights of Heegner cycles and derivatives of L …

Did you know?

WebColmez’s conjecture has been used by Tsimerman [Ts] to provide an unconditional proof of the Andr e-Ort conjecture for abelian varieties of Hodge type. Around the same time as [AGHMP2] also X. Yuan and S.-W. Zhang [YZ] proved, using di erent techniques, the averaged form of Colmez’s conjecture. 2 The average Colmez conjecture WebWe give a proof of the André-Oort conjecture for $\mathcal {A}_g$ — the moduli space of principally polarized abelian varieties. In particular, we show that a recently proven “averaged” version of the Colmez conjecture yields lower bounds for Galois orbits of CM points. The André-Oort conjecture then follows from previous work of Pila and the author.

WebThe André-Oort conjecture for $\mathcal {A}_g$ ... Benjamin Howard, Keerthi Madapusi Pera. On the averaged Colmez conjecture. Pages 533-638 by Xinyi Yuan, Shou-Wu Zhang. Search for: Online Content on Project Euclid 2024–2024. Online Content on JSTOR 1884--2024. To appear in forthcoming issues. 2024. Webthe proof of an averaged version of Colmez's conjecture. This book thus blends initiation to fundamental tools of Arakelov geometry with original material corresponding to current research. This book will be particularly useful for graduate students and researchers interested in the connections between algebraic geometry and number theory.

Web1 de jan. de 2024 · The Colmez conjecture, proposed by Colmez, is a conjecture expressing the Faltings height of a CM abelian variety in terms of some linear … WebThe Colmez conjecture is a formula expressing the Faltings height of an abelian variety with complex multiplication in terms of some linear combination of logarithmic derivatives …

Web24 de jul. de 2015 · The Colmez conjecture, proposed by Colmez, is a conjecture expressing the Faltings height of a CM abelian variety in terms of some linear combination of logarithmic derivatives of Artin L-functions. The aim of this paper to prove an averaged version of the conjecture.

Web1 de nov. de 2024 · This is an expository article on the averaged version of Colmez's conjecture, relating Faltings heights of CM abelian varieties to Artin L-functions. It is … simulate overlay filter with cssWeb8 de fev. de 2024 · As an application of this result, we prove an averaged version of Colmez's conjecture on the Faltings heights of CM abelian varieties, up to a bounded rational multiple of log(2). rcvd hpWebThis is an expository article on the averaged version of Colmez's conjecture, relating Faltings heights of CM abelian varieties to Artin L-functions. It is based on the … rcvd gi high fiberWeb1114-11-142 Xinyi Yuan* ([email protected]), Berkeley, CA 94702. On the Averaged Colmez Conjecture. The Colmez conjecture expresses the Faltings height of a CM abelian variety in terms of the logarithmic derivatives of certain Artin L-functions. In this talk, I will present an averaged version of the conjecture proved in my joint work with rcvd in pharmaWebThe Colmez conjecture expresses the Faltings height of a CM abelian variety in terms of the logarithmic derivatives of certain Artin L-functions. In this talk, I will present an … rcvd hydrolyzed protein for cats simulate nuggs microwaveWeb27 de set. de 2024 · Download PDF Abstract: The well-known 1-2-3 Conjecture asserts that the edges of every graph without isolated edges can be weighted with $1$, $2$ and $3$ … simulate network traffic