Lifting Galois representations via Galois cohomology

TL;DR

This survey reviews recent advances in lifting Galois representations using Galois cohomology, highlighting approaches discussed at a 2024 conference honoring Ján Mináč's contributions.

Contribution

It compiles and discusses recent progress in lifting Galois representations through Galois cohomology, emphasizing approaches presented at a major conference.

Findings

Summarizes key methods relying solely on Galois cohomology.

Highlights recent theoretical developments in the field.

Connects progress to ongoing research discussions.

Abstract

This is a survey paper, on recent progress around lifting Galois representations. I focused on approaches that solely rely on Galois cohomology. Emphasis is laid on material I talked about, at the conference held in Ottawa in June 2024, to celebrate J\'an Min\'a\v{c}'s 71th birthday.