Brauer-Siegel for arithmetic tori and lower bounds for Galois orbits of special points
@article{Tsimerman2011BrauerSiegelFA,
title={Brauer-Siegel for arithmetic tori and lower bounds for Galois orbits of special points},
author={Jacob Tsimerman},
journal={Journal of the American Mathematical Society},
year={2011},
volume={25},
pages={1091-1117}
}In \cite{S}, Shyr derived an analogue of Dirichlet's class number formula for arithmetic Tori. We use this formula to derive a Brauer-Siegel formula for Tori, relating the Discriminant of a torus to the product of its regulator and class number. We apply this formula to derive asymptotics and lower bounds for Galois orbits of CM points in the Siegel modular variety $A_{g,1}$. Specifically, we ask that the sizes of these orbits grows like a power of Discriminant of the underlying endomorphism… CONTINUE READING
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