Seminar by Joachim Kock (Universitat Autònoma de Barcelona)

Title: Point-free topology and Hochster duality in derived categories

2017.05.03 | Christine Dilling

Date Mon 08 May
Time 14:30 15:30
Location 1531-215 Aud. D3


A classical theorem of Hopkins, Neeman and Thomason can be stated in the following conceptual way. For R a commutative ring, the compactly generated localising subcategories of D(R) form a coherent frame, Hochster dual to the Zariski frame (the frame of radical ideals in R). I'll explain the statement through a brief introduction to point-free topology, and explain how it relates to the original formulation. I'll sketch the proof which exploits cellularisation techniques. Next I'll explain how also the Zariski frame itself can be realised inside D(R). Finally I'll comment on the global case, Thomason's theorem for coherent schemes (i.e. quasi-separated and quasi-compact), whose proof in this approach is related to recent developments in constructive algebraic geometry. This is joint work with Wolfgang Pitsch.