From Ohkawa to strong generation via approximable triangulated categories -- a variation on the theme of Amnon Neeman's Nagoya lecture series

TL;DR

This survey introduces the concept of approximable triangulated categories, providing background and motivation to understand Neeman's recent work on strong generation criteria, connecting foundational theorems with advanced research.

Contribution

It offers a comprehensive overview and technical details to facilitate understanding of Neeman's recent results on strong generation in triangulated categories, especially for non-experts.

Findings

Clarifies the role of Ohkawa's theorem in triangulated categories

Explains Neeman's criteria for strong generation using de Jong's regular alteration

Connects foundational results with recent advances in the field

Abstract

This survey stems from Amnon Neeman's lecture series at Ohakawa's memorial workshop. Starting with Ohakawa's theorem, this survey intends to supply enough motivation, background and technical details to read Neeman's recent papers on his "approximable triangulated categories" and his $D_{coh}^b(X)$ strong generation sufficient criterion via de Jong's regular alteration, even for non-experts. At the same time, the author, who happens to be a coorganizer of this workshop and an editor of the follow-up proceedings to be published as a series in Springer Proceedings in Mathematics and Statistics, repeatedly mentioned rich mathematical interaction with other papers in the proceedings, whenever appropriate.