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SUMMARY:The homotopy theory of ideals in stable model categories - David  
 White (Denison University)
DTSTART:20240617T154500Z
DTEND:20240617T161500Z
UID:TALK217804@talks.cam.ac.uk
DESCRIPTION:In 2006\, Jeff Smith gave a talk explaining how to define idea
 ls in the context of ring spectra\, and laying out applications to algebra
 ic K-theory computations. In 2014\, Mark Hovey posted a preprint working o
 ut the homotopy theory of such ideals\, in any stable model category. Sinc
 e every map is homotopic to an inclusion\, ideals must be defined diagramm
 atically rather than as subobjects. In this talk\, I will explain the defi
 nition\, and then discuss joint work with Donald Yau that extends Hovey&rs
 quo\;s work to develop a homotopy theory of ideals with additional structu
 re encoded by an operad. I&rsquo\;ll unpack the definition in algebraic se
 ttings like chain complexes and the stable module category. If there&rsquo
 \;s time\, I&rsquo\;ll discuss applications to algebraic K-theory and othe
 r localizing invariants\, and open problems.
LOCATION:External
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