Lifting of Abelian Covers from Characteristic $p$ to Characteristic $0$

Thời gian: 16h30 thứ Năm ngày 12/06/2025

Địa điểm: Room 612, A6, Institute of Mathematics-VAST

Online (Join Zoom Meeting) tại link: https://zoom.us/j/99636681387?pwd=0WscBnehOJig68SqctGluVuA3RwraE.1

Tóm tắt: In characteristic $0$, it is known that cyclic extensions of fields are determined by Kummer theory. In characteristic $p$, 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 $p$ and characteristic $0$. In this talk, we discuss an algebraization process of Matsuda’s theory to study the lifting of abelian isogenies from characteristic $p$ to characteristic $0$ 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.