Noncommutative counterparts of celebrated conjectures

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.

arXiv commentSurvey article; 23 pages. Revised version. arXiv admin note: text overlap with arXiv:1808.00950