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

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.

68 page Version 3 with very minor revision: two more references and a relevant footnote have been added. Final version will appear in Bousfield Classes and Ohkawa's Theorem -- Nagoya, Japan, August 28--30, 2015, a series in Springer Proceedings in Mathematics and Statistics

References in corpus (11)

• Higher Topos Theory
• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Tannaka Duality for Geometric Stacks
• Chromatic splitting for the $K(2)$-local sphere at $p=2$
• The telescope conjecture for algebraic stacks
• Completing perfect complexes
• Strong generators in $D^{perf}(X)$ and $D_{coh}^b(X)$
• Birational geometry and derived categories
• The algebraic chromatic splitting conjecture for Noetherian ring spectra
• The categories ${\mathcal{T}}^c$ and ${\mathcal{T}}_c^b$ determine each other
• A remark on Hopkins' chromatic splitting conjecture