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.
Second author supported by NSF Grant
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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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