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Canonical Lifts of Families of Elliptic Curves

Borger, James; Gurney, Lance


We show that the canonical lift construction for ordinary elliptic curves over perfect fields of characteristic extends uniquely to arbitrary families of ordinary elliptic curves, even over -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,...[Show more]

CollectionsANU Research Publications
Date published: 2019
Type: Journal article
Source: Nagoya Mathematical Journal
DOI: 10.1017/nmj.2017.34


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