Infinite extensions with finitely many CM moduli
Shu Kawaguchi, Fabien Pazuki

TL;DR
This paper demonstrates the existence of uncountably many algebraic extensions of the rational numbers that contain only finitely many moduli of CM simple principally polarized abelian varieties for any fixed dimension, extending previous results in dimension 1.
Contribution
It generalizes Hultberg's result from dimension 1 to higher dimensions, showing the abundance of such algebraic extensions.
Findings
Uncountably many algebraic extensions with finitely many CM moduli exist for any dimension.
Extension of Hultberg's dimension 1 result to higher dimensions.
Finiteness of CM moduli in these extensions is established.
Abstract
We show that there are uncountably many algebraic extensions of containing at most finitely many moduli of CM simple principally polarized abelian varieties of any fixed dimension , generalizing a result of Hultberg in dimension 1.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Topology and Set Theory · Rings, Modules, and Algebras
