Geodesic
Brauer-Siegel for arithmetic tori and lower bounds for Galois orbits of special points
Tsimerman, Jacob1, 2
1 Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000
2 Department of Mathematics, Faculty of Arts & Sciences, Harvard University, One Oxford Street, Cambridge MA 02138
Journal of the American Mathematical Society, Tome 25 (2012) no. 4, pp. 1091-1117

Voir la notice de l'article provenant de la source American Mathematical Society

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 grow like a power of the discriminant of the underlying endomorphism algebra. We prove this unconditionally in the case $g\leq 6$, and for all $g$ under the Generalized Riemann Hypothesis for CM fields. Along the way we derive a general transfer principle for torsion in ideal class groups of number fields.
DOI : 10.1090/S0894-0347-2012-00739-5

Tsimerman, Jacob 1, 2

1 Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000
2 Department of Mathematics, Faculty of Arts & Sciences, Harvard University, One Oxford Street, Cambridge MA 02138 
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Tsimerman, Jacob. Brauer-Siegel for arithmetic tori and lower bounds for Galois orbits of special points. Journal of the American Mathematical Society, Tome 25 (2012) no. 4, pp. 1091-1117. doi: 10.1090/S0894-0347-2012-00739-5

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