Smallness of Faltings heights of CM abelian varieties

@article{Wei2022SmallnessOF,
  title={Smallness of Faltings heights of CM abelian varieties},
  author={Xunjing Wei},
  journal={Journal of Number Theory},
  year={2022}
}
  • Xunjing Wei
  • Published 31 October 2021
  • Mathematics
  • Journal of Number Theory

References

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Let M be the Shimura variety associated with the group of spinor similitudes of a rational quadratic space over of signature (n,2). We prove a conjecture of Bruinier-Kudla-Yang, relating the

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Colmez conjectured a product formula for periods of abelian varieties with complex multiplication by a field $$K$$, analogous to the standard product formula in algebraic number theory. He proved

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In w 1 we consider the situation: L/K is a finite separable field extension, A is an abelian variety over L, and A, is the abelian variety over K obtained from A by restriction of scalars. We study

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Let k be an algebraic number field of degree n~ and discriminant D~. We let Kk denote the residue of ~(s), " " the zeta function of k, at s = 1. One version of the Brauer-Siegel Theorem is that if k

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The purpose of this chapter is to give a brief introduction to the moduli spaces of abelian varieties and their compactification. Only the geometric aspects of the theory are discussed. The

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  • Mathematics
    Compositio Mathematica
  • 1998
Motivated by a result of Bost, we use the relationship between Faltings' heights of abelian varieties with complex multiplication and logarithmic derivatives of Artin L-functions at s=0 to

On Faltings heights of abelian varieties with complex multiplication

This expository article introduces some conjectures and theorems related to the Faltings heights of abelian varieties with complex multiplication. The topics include the Colmez conjecture, the

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Algebraic groups play much the same role for algebraists as Lie groups play for analysts. This book is the first comprehensive introduction to the theory of algebraic group schemes over fields that

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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.

NÉRON MODELS

§1.1. Motivation. The purpose of these notes is to explain the definition and basic properties of the Néron model A of an abelian variety A over a global or local field K. We also give some idea of