A universal formula for the j-invariant of the canonical lifting

作者：Erdogan Altan^*

来源：Journal of Number Theory, 2015, 150: 26-40.

DOI：10.1016/j.jnt.2014.11.002

• Elliptic curves
• Serre-Tate theorem
• Canonical lifting

We study the j-invariant of the canonical lifting of an elliptic curve as a Witt vector. We prove that its Witt coordinates lie in an open affine subset of the j-line and deduce the existence of a universal formula for the j-invariant of the canonical lifting. The canonical lifting of the elliptic curves with j-invariant 0 and 1728 over any characteristic is also explicitly found.

• 出版日期2015-5