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Title: Abelian varieties with everywhere good reduction over certain real quadratic fields of small discriminant.

abstract:聽Let $F = Q(sqrt{D})$, where $D = 53, 61$ or $73$. There is a simple abelian surface $A/F$ with everywhere good reduction. Under GRH, we show that every abelian variety with everywhere good reduction is isogenous to a power of $A$. This result extends previous work of Fontaine and Schoof.