# From Ohkawa to Strong Generation via Approximable Triangulated Categories—A Variation on the Theme of Amnon Neeman’s Nagoya Lecture Series

@article{Minami2020FromOT, title={From Ohkawa to Strong Generation via Approximable Triangulated Categories—A Variation on the Theme of Amnon Neeman’s Nagoya Lecture Series}, author={Norihiko Minami}, journal={Bousfield Classes and Ohkawa's Theorem}, year={2020} }

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…

## References

SHOWING 1-10 OF 151 REFERENCES

The K -Theory of Triangulated Categories

- Mathematics
- 2005

Centre for Mathematics and its Applications Mathematical Sciences Institute John Dedman Building The Australian National University Canberra, ACT 0200 AUSTRALIA Amnon.Neeman@anu.edu.au Summary. The…

Approximable triangulated categories

- Mathematics
- 2018

In this survey we present the relatively new concept of \emph{approximable triangulated categories.} We will show that the definition is natural, that it leads to powerful new results, and that it…

Triangulated categories of motives in positive characteristic

- Mathematics
- 2012

This thesis presents a way to apply this theorem of Gabber to a large portion of Voevodsky's work in order to lift the assumption that resolution of singularities holds. This gives unconditional…

Stability conditions on triangulated categories

- Mathematics
- 2002

This paper introduces the notion of a stability condition on a triangulated category. The motivation comes from the study of Dirichlet branes in string theory, and especially from M.R. Douglas's…

The Grothendieck duality theorem via Bousfield’s techniques and Brown representability

- Mathematics
- 1996

Grothendieck proved that if f: X ) Y is a proper morphism of nice schemes, then Rf* has a right adjoint, which is given as tensor product with the relative canonical bundle. The original proof was by…

Smashing subcategories and the telescope conjecture – an algebraic approach

- Mathematics
- 2000

Abstract.We prove a modified version of Ravenel’s telescope conjecture. It is shown that every smashing subcategory of the stable homotopy category is generated by a set of maps between finite…

Nilpotence and Periodicity in Stable Homotopy Theory.

- Mathematics
- 1992

"Nilpotence and Periodicity in Stable Homotopy Theory" describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were…

Completing perfect complexes

- MathematicsMathematische Zeitschrift
- 2020

This note proposes a new method to complete a triangulated category, which is based on the notion of a Cauchy sequence. We apply this to categories of perfect complexes. It is shown that the bounded…