论文标题
带有小芒福德群体的超级阳离子阿伯利亚品种的升降机
Lifts of supersingular abelian varieties with small Mumford-Tate groups
论文作者
论文摘要
我们调查了有限领域的阿贝里亚人在多大程度上可以通过小型蒙福德（Mumford-tate）组提起一个特征零的一个。我们证明，可以分别将超代数的Abelian表面提升为椭圆曲线的正方形的正方形。另一方面，我们表明，超级有源的阿贝尔三倍不能将其抬高到一个椭圆曲线的立方体上，而椭圆形曲线上的矢量也无法提起。
We investigate to what extent an abelian variety over a finite field can be lifted to one in characteristic zero with small Mumford-Tate group. We prove that supersingular abelian surfaces, respectively threefolds, can be lifted to ones isogenous to a square, respectively product, of elliptic curves. On the other hand, we show that supersingular abelian threefolds cannot be lifted to one isogenous to the cube of an elliptic curve over the Witt vectors.
