Signature $(n-2,2)$ CM Types and the Unitary Colmez Conjecture

Solly Parenti

Signature $(n-2,2)$ CM Types and the Unitary Colmez Conjecture

Number Theory 2018-03-08 v1

Authors: Solly Parenti

Abstract

Colmez conjectured a formula relating the Faltings height of CM abelian varieties to a certain linear combination of log derivatives of $L$ -functions. In this paper, we study the case of unitary CM fields and by studying the class functions that arise, we reduce the conjecture to a special case. Using the Galois action, we prove more cases of the Colmez Conjecture.

Keywords

colmez conjecture cm abelian varieties faltings height unitary cm fields l-functions galois action

Cite

@article{arxiv.1803.02535,
  title  = {Signature $(n-2,2)$ CM Types and the Unitary Colmez Conjecture},
  author = {Solly Parenti},
  journal= {arXiv preprint arXiv:1803.02535},
  year   = {2018}
}

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