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<p>In this short note we show that Galois orbits of CM points equidistribute on a product of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(r\geqslant 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>r</mi> <mo>⩾</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> non-isomorphic Shimura curves by applying the adelic toral-packet equidistribution theorem of Aka–Luethi–Michel–Wieser. As a consequence, we deduce André–Oort for the product of those curves, previously studied by Edixhoven and Yafaev, replacing GRH by a Linnik-type splitting condition at two auxiliary primes.</p>

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A note on equidistribution on a product of Shimura curves and André–Oort

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  • 发表日期：

    2026年7月9日

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  • Francesco Maria Saettone

摘要

In this short note we show that Galois orbits of CM points equidistribute on a product of \(r\geqslant 2\) r ⩾ 2 non-isomorphic Shimura curves by applying the adelic toral-packet equidistribution theorem of Aka–Luethi–Michel–Wieser. As a consequence, we deduce André–Oort for the product of those curves, previously studied by Edixhoven and Yafaev, replacing GRH by a Linnik-type splitting condition at two auxiliary primes.