The refined lifting problem for Galois coverings
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  • The refined lifting problem for Galois coverings

The refined lifting problem for Galois coverings

Thời gian: 14:00 đến 15:30 Ngày 25/10/2022

Địa điểm: C102, VIASM

Báo cáo viên: Đặng Quốc Huy

Tóm tắt:
The local lifting problem asks: for k a field of characteristic p>0, which finite Galois extensions of k[[t]] "lift" to characteristic zero? A breakthrough in the domain happened in 2014 when Obus–Wewers and Pop's combined effort proved that any extension with cyclic Galois group does. However, many important questions remain unanswered. Among those is a question proposed by Saïdi, the so-called refined lifting problem, about the lift-ability of extensions "in towers".
After giving an introduction to the lifting problem as well as some useful techniques, we will discuss our answer for a general case when the characteristic is 2 and propose some directions for generalizing that result.