Lifting of Curves

TL;DR

This paper proves the Oort Conjecture in the general case by combining recent results and deformation techniques in characteristic p, also providing a boundedness result.

Contribution

It offers a new proof of the Oort Conjecture using a special case of Obus-Wewers' result and deformation arguments, advancing understanding in algebraic geometry.

Findings

Proof of the Oort Conjecture in the general case

Establishment of a boundedness result

Application of deformation techniques in characteristic p

Abstract

In this note we show that a special case of a recent result by Obus-Wewers (used as a black box) together with a deformation argument in characteristic $p$ leads to a proof of the Oort Conjecture in the general case. A boundedness result is given as well.