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

Solly Parenti

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arXiv · 1803.02535

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

Solly Parenti

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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.

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Solly Parenti. 2018-03-07. Signature $(n-2,2)$ CM Types and the Unitary Colmez Conjecture. https://arxiv.org/abs/1803.02535

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