3 citations · 7 across the 8 of their papers we have counts for
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On abelian surfaces with potential quaternionic multiplication
Luis Dieulefait, Victor Rotger
An abelian surface A over a field K has potential quaternionic multiplication if the ring End_\bar K (A) of geometric endomorphisms of A is an order in an indefinite rational divis…
The field of moduli of quaternionic multiplication on abelian varieties
Victor Rotger
We consider principally polarized abelian varieties with quaternionic multiplication over number fields and we study the field of moduli of their endomorphisms in relation to the s…
Failure of the Hasse principle for Atkin-Lehner quotients of Shimura curves over \Q
V. Rotger, A. Skorobogatov, A. Yafaev
We show how to construct counter-examples to the Hasse principle over the field of rational numbers on Atkin-Lehner quotients of Shimura curves and on twisted forms of Shimura curv…
Easy decision-Diffie-Hellman groups
Steven Galbraith, Victor Rotger
The decision-Diffie-Hellman problem (DDH) is a central computational problem in cryptography. It is known that the Weil and Tate pairings can be used to solve many DDH problems on…
Shimura curves embedded in Igusa's threefold
Victor Rotger
Let O be a maximal order in a totally indefinite quaternion algebra over a totally real number field. In this note we study the locus Q_O of quaternionic multiplication by O in the…
The arithmetic of QM-abelian surfaces through their Galois representations
Luis V. Dieulefait, V. Rotger
This note provides an insight to the diophantine properties of abelian surfaces with quaternionic multiplication over number fields. We study the fields of definition of the endomo…