# Noncommutative counterparts of celebrated conjectures

## TL;DR

This survey explores the noncommutative analogues of major conjectures in algebraic geometry and related fields, providing a comprehensive overview of recent developments and open problems.

## Contribution

It systematically reviews the noncommutative versions of renowned conjectures, highlighting their significance and current status in mathematical research.

## Key findings

- Summarizes key noncommutative conjectures and their implications.
- Identifies open problems and directions for future research.
- Connects classical conjectures with their noncommutative counterparts.

## Abstract

In this survey, written for the proceedings of the conference K-theory in algebra, analysis and topology, Buenos-Aires, Argentina (satellite event of the ICM 2018), we give a rigorous overview of the noncommutative counterparts of some celebrated conjectures of Grothendieck, Voevodsky, Beilinson, Weil, Tate, Parshin, Kimura, Schur, and others.