University of Illinois Urbana-Champaign

Stabilizing spectral functors of exact categories

Villeta-Garcia, Juan S

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VILLETA-GARCIA-DISSERTATION-2017.pdf

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https://hdl.handle.net/2142/98290

Description

Title
Stabilizing spectral functors of exact categories
Author(s)
Villeta-Garcia, Juan S
Issue Date
2017-07-13
Director of Research (if dissertation) or Advisor (if thesis)
McCarthy, Randy
Doctoral Committee Chair(s)
Ando, Matthew
Committee Member(s)
  • Rezk, Charles
  • Malkiewich, Cary
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2017-09-29T17:52:21Z
Keyword(s)
  • Algebraic K-theory
  • Goodwillie calculus
  • Homotopy theory
  • Algebraic topology
Abstract
We define and study the $K$-theory of exact categories with coefficients in endofunctors of spectra in analogy with Mitchell's homology of categories. Generalizing computations of McCarthy, we determine, for a discrete ring $R$, the $K$-theory of the exact category of finitely-generated projective $R$-modules with coefficients in the $n$-fold smash product functor. This computation allows us to analyze the effects of applying this functorial construction to the Goodwillie Taylor tower of a homotopy endofunctor of spectra. In the case of $\Sigma^\infty\Omega^\infty$, the associated tower recovers the Taylor tower of relative $K$-theory as computed by Lindenstrauss and McCarthy.
Graduation Semester
2017-08
Type of Resource
text
Permalink
http://hdl.handle.net/2142/98290
Copyright and License Information
Copyright 2017 Juan Villeta-Garcia

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