Categorification at prime roots of unity and hopfological finiteness

TL;DR

This paper surveys recent advances in hopfological algebra and categorification at prime roots of unity, focusing on the properties of the Jones-Wenzl projector and its finiteness in different characteristics.

Contribution

It demonstrates that the categorical Jones-Wenzl projector is hopfologically finite in special characteristics but infinite in generic cases, advancing understanding of categorification at roots of unity.

Findings

Jones-Wenzl projector is hopfologically finite in special characteristics

In generic characteristics, the projector is infinite

Provides insights into categorification at prime roots of unity

Abstract

We survey some recent results in hopfological algebra and the program of categorification at prime roots of unity. A categorical Jones-Wenzl projector at prime roots of unity is studied, and it is shown that this projector is hopfologically finite in special characteristics, while generically it is infinite.