CANONICAL LIFTS OF FAMILIES OF ELLIPTIC CURVES
Published online by Cambridge University Press: 02 November 2017
We show that the canonical lift construction for ordinary elliptic curves over perfect fields of characteristic $p>0$ extends uniquely to arbitrary families of ordinary elliptic curves, even over $p$-adic formal schemes. In particular, the universal ordinary elliptic curve has a canonical lift. The existence statement is largely a formal consequence of the universal property of Witt vectors applied to the moduli space of ordinary elliptic curves, at least with enough level structure. As an application, we show how this point of view allows for more formal proofs of recent results of Finotti and Erdoğan.
- Nagoya Mathematical Journal , Volume 233 , March 2019 , pp. 193 - 213
- © 2017 Foundation Nagoya Mathematical Journal