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December 2005 On abelian surfaces with potential quaternionic multiplication
Luis V. Dieulefait, Victor Rotger
Bull. Belg. Math. Soc. Simon Stevin 12(4): 617-624 (December 2005). DOI: 10.36045/bbms/1133793348

Abstract

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 division quaternion algebra. In this brief note, we study the possible structures of the ring of endomorphisms of these surfaces and we provide explicit examples of Jacobians of curves of genus two which show that our result is sharp.

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Luis V. Dieulefait. Victor Rotger. "On abelian surfaces with potential quaternionic multiplication." Bull. Belg. Math. Soc. Simon Stevin 12 (4) 617 - 624, December 2005. https://doi.org/10.36045/bbms/1133793348

Information

Published: December 2005
First available in Project Euclid: 5 December 2005

zbMATH: 1146.11033
MathSciNet: MR2206004
Digital Object Identifier: 10.36045/bbms/1133793348

Subjects:
Primary: 11G18, 14G35

Rights: Copyright © 2005 The Belgian Mathematical Society

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Vol.12 • No. 4 • December 2005
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