Non-existence of certain CM abelian varieties with prime power torsion
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In this article, a conjecture of Rasmussen and Tamagawa, on the finiteness of the set of isomorphism classes of abelian varieties with constrained prime power torsion was studied.Abstract:
In this paper, we study a conjecture of Rasmussen and Tamagawa, on the finiteness of the set of isomorphism classes of abelian varieties with constrained prime power torsion. Our result is related with abelian varieties which have complex multiplication over their fields of definition.read more
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Algebraic points on Shimura curves of Γ0(p)-type (II)
TL;DR: In this paper, it was shown that for a quadratic field, there are at most elliptic points on a Shimura curve of Γ 0(p)-type for every sufficiently large prime number p.
Galois images and modular curves
TL;DR: In this article, the authors present a survey of the Galois representations associated to elliptic curves and QM-abelian surfaces, including rational points, points over quadratic fields on modular curves and Shimura curves.
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Algebraic points on Shimura curves of $\Gamma_0(p)$-type (III)
Keisuke Arai,Fumiyuki Momose +1 more
TL;DR: In this article, it was shown that there are at most elliptic points on such a Shimura curve for every sufficiently large prime number $p, and a similar result for points over number fields of higher degree on Shimura curves of the same type.
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On the Rasmussen-Tamagawa conjecture for QM-abelian surfaces
TL;DR: In this article, the Rasmussen-Tamagawa conjecture for QM-abelian surfaces over imaginary quadratic fields has been generalized to higher degree fields, and several explicit examples have been given.
Journal ArticleDOI
Algebraic points on Shimura curves of Γ0(p)-type
Keisuke Arai,Fumiyuki Momose +1 more
TL;DR: In this paper, it was shown that for a quadratic field, there are at most elliptic points on a Shimura curve of Γ0(p)-type for every sufficiently large prime number p. This is an analogue of the study of rational points on the modular curve X 0(p).
References
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