On the averaged colmez conjecture
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 … Web1114-11-142 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
On the averaged colmez conjecture
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WebThe Colmez conjecture, proposed by Colmez [Co], is a conjecture expressing the Faltings height of a CM abelian variety in terms of some linear combination of … 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.
Web19 de nov. de 2024 · As applications of the second sum above, we consider the averaged version of Erdős–Turán's conjecture and the equation a + b = c. In particular, we show … http://faculty.bicmr.pku.edu.cn/~yxy/preprints/averaged_colmez.pdf
Web27 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 $3$ … 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 …
WebThis 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 …
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 of Artin L -functions. The aim of this paper to prove an averaged version of the conjecture, … is that any goodWebWhen 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. iget thanosWeb1 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 … i get szve when i try to printWebKEYWORDS: André-Oort, Complex Multiplication, Faltings height, Colmez conjecture, 11G15, 11G18 Read Abstract + We give a proof of the André-Oort conjecture for $\mathcal{A}_g$ --- the moduli space of principally polarized abelian varieties. is that any way for a man to carry onWebthe 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. i get that all the timeWeb8 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). i get termours whenWeba recently proven \averaged" version of the Colmez conjecture yields lower bounds for Galois orbits of CM points. The Andr e-Oort conjecture then follows from previous work of Pila and the author. 1. Introduction Recall the statement of the Andr e-Oort conjecture: Conjecture 1.1. Let Sbe a Shimura variety, and let V be an irreducible is that any way to run an airline