Cellularization of D(R) and point-free reconstruction of affine schemes
Event details
| Date | 08.02.2013 |
| Hour | 14:15 › 15:30 |
| Speaker | Wolfgang Pitsch (UA Barcelona) |
| Location |
MA 30
|
| Category | Conferences - Seminars |
In this talk we will revisit the classification of compactly generated localizing subcategories in the derived category of a ring D(R) by Thomason, Neeman, Balmer. We will show how the description of cellularization in D(R) with respect to quotients R/I of the ring by a finitely generated ideal, due to Dwyer-Greenlees, leads to a natural bijection between the lattice of compactly generated localizing subcategories and the Hochster open sets in Spec R, avoiding almost all noetherian assumptions. We will show in particular that the algebraic version of the "nilpotence theorem'' of Devinatz, Hopkins and Smith is in fact a consequence of the fact that Spec R with this topology is a Tychonoff space. If time permits we will show how to dualize this construction in D(R) to reconstruct the usual affine scheme Spec R.
This is joint work with Joachim Kock (Universidad Autonoma de Barcelona)
This is joint work with Joachim Kock (Universidad Autonoma de Barcelona)
Links
Practical information
- Informed public
- Free
Organizer
- Kathryn Hess (EPFL)