Motivic symmetric ring spectrum representing algebraic K-theory
Kim, Youngsoo
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https://hdl.handle.net/2142/16878
Description
Title
Motivic symmetric ring spectrum representing algebraic K-theory
Author(s)
Kim, Youngsoo
Issue Date
2010-08-20T18:00:36Z
Director of Research (if dissertation) or Advisor (if thesis)
Grayson, Daniel R.
Doctoral Committee Chair(s)
McCarthy, Randy
Committee Member(s)
Grayson, Daniel R.
Ando, Matthew
Rezk, Charles
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
motivic spectrum
algebraic K-theory
ring spectrum
standard vector bundles
Abstract
Voevodsky showed that there is a motivic spectrum representing algebraic K-theory. We describe an equivalent spectrum that is also a symmetric ring spectrum. A coherence problem occurs when one verifies the symmetry. It is explained and solved by introducing a category of vector bundles with strictly associative tensor product that is also strictly commutative with line bundles.
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