$K$-theory of hyperplanes
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- by Barry H. Dayton and Charles A. Weibel PDF
- Trans. Amer. Math. Soc. 257 (1980), 119-141 Request permission
Abstract:
Let R be the coordinate ring of a union of N hyperplanes in general position in ${\textbf {A}}_k^{n + 1}$. Then \[ {K_i}(R) = {K_i}(k) \oplus \left ( {\begin {array}{*{20}{c}} {N - 1} \\ {n + 1} \\ \end {array} } \right ) {K_{n + i}}(k).\] This formula holds for ${K_0}, {K_1}, {K_i} (i < 0)$, and for the Karoubi-Villamayor groups $K{V_i} (i \in {\mathbf {Z}})$. For ${K_2}$ there is an extra summand $\bar R/R$, where $\bar R$ is the normalization of R. For ${K_3}$ the above is a quotient of ${K_3}(R)$. In §4 we show that ${K_1}$-regularity implies ${K_0}$-regularity, answering a question of Bass. We also show that ${K_i}$-regularity is equivalent to Laurent ${K_i}$-regularity for $i \leqslant 1$. The results of this section are independent of the rest of the paper.References
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Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 257 (1980), 119-141
- MSC: Primary 18F25; Secondary 14C35
- DOI: https://doi.org/10.1090/S0002-9947-1980-0549158-6
- MathSciNet review: 549158