Tóm tắt: In characteristic , it is known that cyclic extensions of fields are determined by Kummer theory. In characteristic , in addition to Kummer theory, we need Artin–Schreier–Witt theory to classify these extensions. Matsuda constructed a formal morphism that connects these two theories, providing a bridge between characteristic and characteristic . In this talk, we discuss an algebraization process of Matsuda’s theory to study the lifting of abelian isogenies from characteristic to characteristic and show that every lift of an abelian étale cover of a local scheme is a pull-back of such a lift of an abelian isogeny.