𝑆𝐾₁ of 𝑛 lines in the plane

Roberts, Leslie G.

doi:10.1090/S0002-9947-1976-0422278-1

$SK\sb{1}$ of lines in the plane

Author: Leslie G. Roberts
Journal: Trans. Amer. Math. Soc. 222 (1976), 353-365
MSC: Primary 14F15; Secondary 14C20
DOI: https://doi.org/10.1090/S0002-9947-1976-0422278-1
MathSciNet review: 0422278
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Abstract: We calculate $S{K_1}(A)$ where A is the coordinate ring of the reduced affine variety consisting of n straight lines in the plane.

[1] Sergio Antoy, Sul calcolo del gruppo di Picard di certe estensioni intere semplici, Ann. Univ. Ferrara Sez. VII (N.S.) 18 (1973), 155–167 (Italian, with English summary). MR 0332757
[2] R. K. Dennis and M. Krusemeyer, ${K_2}$ of , a problem of Swan, and related computations (to appear).
[3] R. Keith Dennis and Michael R. Stein, The functor 𝐾₂: a survey of computations and problems, Algebraic 𝐾-theory, II: “Classical” algebraic 𝐾-theory and connections with arithmetic (Proc. Conf., Seattle Res. Center, Battelle Memorial Inst., 1972) Springer, Berlin, 1973, pp. 243–280. Lecture Notes in Math., Vol. 342. MR 0354815
[4] Jimmie Graham, Continuous symbols on fields of formal power series, Algebraic 𝐾-theory, II: “Classical” algebraic 𝐾-theory and connections with arithmetic (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972) Springer, Berlin, 1973, pp. 474–486. Lecture Notes in Math., Vol. 342. MR 0364187
[5] John Labute and Peter Russell, On 𝐾₂ of truncated polynomial rings, J. Pure Appl. Algebra 6 (1975), no. 3, 239–251. MR 0396595, https://doi.org/10.1016/0022-4049(75)90019-5
[6] John Milnor, Introduction to algebraic 𝐾-theory, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1971. Annals of Mathematics Studies, No. 72. MR 0349811
[7] Ferruccio Orecchia, Sui gruppi di Picard di certe algebre finite non integre, Ann. Univ. Ferrara Sez. VII (N.S.) 21 (1975), 25–36. MR 0404258
[8] Leslie G. Roberts, Higher derivations and the Jordan canonical form of the companion matrix, Canad. Math. Bull. 15 (1972), 143–144. MR 0316474, https://doi.org/10.4153/CMB-1972-027-6
[9] Leslie G. Roberts, The 𝐾-theory of some reducible affine varieties, J. Algebra 35 (1975), 516–527. MR 0404259, https://doi.org/10.1016/0021-8693(75)90063-0
[10] Wilberd van der Kallen, Hendrik Maazen, and Jan Stienstra, A presentation for some 𝐾₂(𝑛,𝑅), Bull. Amer. Math. Soc. 81 (1975), no. 5, 934–936. MR 0376818, https://doi.org/10.1090/S0002-9904-1975-13894-8