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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The $K$-theory spectrum of varieties
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by Jonathan A. Campbell PDF
Trans. Amer. Math. Soc. 371 (2019), 7845-7884 Request permission

Abstract:

We produce an $E_\infty$-ring spectrum $K(\mathbf {Var}_{/k})$ whose components model the Grothendieck ring of varieties (over a field $k$) $K_0 (\mathbf {Var}_{/k})$. This is achieved by slightly modifying Waldhausen categories and the Waldhausen $S_\bullet$-construction. As an application, we produce liftings of various motivic measures to spectrum-level maps, including maps into Waldhausen’s $K$-theory of spaces $A(\ast )$ and to $K(\mathbf {Q})$.
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Additional Information
  • Jonathan A. Campbell
  • Affiliation: Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, Tennessee 37240
  • Email: j.campbell@vanderbilt.edu
  • Received by editor(s): January 9, 2017
  • Received by editor(s) in revised form: February 14, 2018, February 28, 2018, and March 23, 2018
  • Published electronically: February 14, 2019
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 371 (2019), 7845-7884
  • MSC (2010): Primary 19D99
  • DOI: https://doi.org/10.1090/tran/7648
  • MathSciNet review: 3955537