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20072024
most citedOn the Rasmussen-Tamagawa conjecture for QM-abelian surfaces

3 citations · 6 across the 11 of their papers we have counts for

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Showing 2014Show all

2 papers · 1 filter

math.NT2014

Points on Shimura curves rational over imaginary quadratic fields in the non-split case

Keisuke Arai

For an imaginary quadratic field of class number , we prove that there are only finitely many isomorphism classes of rational indefinite quaternion division algebras su…

math.NT2014★ 1 cited

Non-existence of points rational over number fields on Shimura curves

Keisuke Arai

Jordan, Rotger and de Vera-Piquero proved that Shimura curves have no points rational over imaginary quadratic fields under a certain assumption. In this article, we expand their r…