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SUMMARY:Cellularization of D(R) and point-free reconstruction of affine sc
 hemes
DTSTART:20130208T141500
DTEND:20130208T153000
DTSTAMP:20260511T072939Z
UID:a770854b164f1b7898ed75a674809f0c54e2241e8808baea21fa63cd
CATEGORIES:Conferences - Seminars
DESCRIPTION:Wolfgang Pitsch (UA Barcelona)\nIn this talk we will revisit t
 he classification of compactly generated localizing subcategories in the d
 erived 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\, l
 eads to a natural bijection between the lattice of compactly generated loc
 alizing subcategories and the Hochster open sets in Spec R\, avoiding almo
 st all noetherian assumptions. We will show in particular that the algebra
 ic 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 Tyc
 honoff space. If time permits we will show how to dualize this constructio
 n in D(R) to reconstruct the usual affine scheme Spec R.\nThis is joint wo
 rk with Joachim Kock (Universidad Autonoma de Barcelona)
LOCATION:MA 30
STATUS:CONFIRMED
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