一个p-幂次无等平凡因子的格自同构的普通阿贝尔簇
An ordinary abelian variety with an etale self-isogeny of p-power degree and no isotrivial factors
摘要：
对每一个素数p，我们构造了一个特征为p的函数域K和一个不含等平凡因子的K上的普通阿贝尔簇A，它容许p次的标准自同构.由此，我们推论出在极大纯不可分扩张上的点群不是可分生成的函数域上存在普通的阿贝尔簇，从而否定地回答了Thomas Scanlon的一个问题.
英文摘要：
We construct, for every prime p, a function field K of characteristic p and an ordinary abelian variety A over K, with no isotrivial factors, that admits an etale self-isogeny of p-power degree. As a consequence, we deduce that there exist ordinary abelian varieties over function fields whose groups of points over the maximal purely inseparable extension is not finitely generated, answering in the negative a question of Thomas Scanlon.
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