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SUMMARY:Nikolas Schonsheck (Ohio State University)
DTSTART:20200606T194000Z
DTEND:20200606T200000Z
DTSTAMP:20260423T022732Z
UID:GOATS/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GOATS/8/">Fi
 bration Theorems for TQ-Completion of Structured Ring Spectra</a>\nby Niko
 las Schonsheck (Ohio State University) as part of GOATS\n\n\nAbstract\nBy 
 considering algebras over an operad $\\mathcal{O}$ in one's preferred cate
 gory of spectra\, we can encode various flavors of algebraic structure (e.
 g. commutative ring spectra). \n    Drawing intuition from singular homolo
 gy of spaces and Quillen homology of rings\, topological Quillen ($\\mathb
 f{TQ}$) homology is a naturally occurring notion of homology for these obj
 ects\, with analogies to both singular homology and stabilization of space
 s. \n\n    For a given $\\mathcal{O}$algebra $X$\, there is a canonical wa
 y (following Bousfield-Kan) to "glue together" iterates $\\mathbf{TQ}^n(X)
 $ of the $\\mathbf{TQ}$-homology spectrum of $X$ to construct "the part of
  $X$ that $\\mathbf{TQ}$-homology sees\," namely its $\\mathbf{TQ}$-comple
 tion. \n    We then ask\, "When can $X$ be 'recovered from' $\\mathbf{TQ}(
 X)$ in this way?" \n    \n    Bousfield-Kan consider the analogous questio
 n in spaces and conclude that all nilpotent spaces are weakly equivalent t
 o their homology completion. \n    The key technical maneuver of their pro
 of involves showing that certain fibration sequences are preserved by comp
 letion. \n    In this talk\, we will discuss certain types of fibration se
 quences of $\\mathcal{O}$-algebras which are preserved by $\\mathbf{TQ}$-c
 ompletion\, drawing analogies along the way to the case of pointed spaces.
 \n
LOCATION:https://researchseminars.org/talk/GOATS/8/
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