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A spectral sequence for the K-theory of affine glued schemes

Part of the Lecture Notes in Mathematics book series (LNM,volume 854)

Abstract

An affine scheme is ‘glued’ if it is the colimit of a finite diagram of affine schemes. We first develop several recognition criteria for determining when an affine scheme is glued. Under mild hypotheses, for example, glued schemes are seminormal. We then investigate the K-theory of glued schemes and develop an Atiyah-Hirzebruch type spectral sequence which converges to the Karoubi-Villamayor K-theory of the glued scheme. This allows us to compute K0 of some interesting rings and generalize a number of previous results in the literature.

Keywords

  • Spectral Sequence
  • Simplicial Complex
  • Commutative Ring
  • Maximal Element
  • Natural Transformation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Second author supported by NSF Grant

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© 1981 Springer-Verlag

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Dayton, B.H., Weibel, C.A. (1981). A spectral sequence for the K-theory of affine glued schemes. In: Friedlander, E.M., Stein, M.R. (eds) Algebraic K-Theory Evanston 1980. Lecture Notes in Mathematics, vol 854. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089516

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  • DOI: https://doi.org/10.1007/BFb0089516

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10698-2

  • Online ISBN: 978-3-540-38646-9

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