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VOL. 30 | 2001 Abelian Varieties over $\mathbf{Q}(\sqrt{6})$ with Good Reduction Everywhere

Abstract

The elliptic curve with Weierstrass equation $Y^2 + \sqrt{6}XY - Y = X^3 - (2 + \sqrt{6})X^2$ has good reduction modulo every prime of the ring of integers of $\mathbf{Q}(\sqrt{6})$. We show that every abelian variety over $\mathbf{Q}(\sqrt{6})$ that has good reduction everywhere is isogenous to a power of this elliptic curve.

Information

Published: 1 January 2001
First available in Project Euclid: 13 September 2018

zbMATH: 1048.11047
MathSciNet: MR1846462

Digital Object Identifier: 10.2969/aspm/03010287

Rights: Copyright © 2001 Mathematical Society of Japan

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