Canonical Lifts of Elliptic Curves Through Witt Vectors

In this thesis, we study the canonical liftings of ordinary elliptic curves over fields of characteristic $p > 0$. Building on the theory of Witt vectors and their relation to the moduli space of ordinary elliptic curves, we show that the canonical lift construction extends to families of ordinary elliptic curves over $p$-adic sheaves. Our approach highlights the formal nature of the construction and its dependence on the universal property of Witt vectors.