$K_{1}$ of a curve of genus zero
HTML articles powered by AMS MathViewer
- by Leslie G. Roberts PDF
- Trans. Amer. Math. Soc. 188 (1974), 319-326 Request permission
Abstract:
We determine the structure of the vector bundles on a curve of genus zero and calculate the “universal determinant” ${K_1}$ of such a curve.References
- Cahit Arf, Untersuchungen über quadratische Formen in Körpern der Charakteristik 2. I, J. Reine Angew. Math. 183 (1941), 148–167 (German). MR 8069, DOI 10.1515/crll.1941.183.148
- M. Atiyah, On the Krull-Schmidt theorem with application to sheaves, Bull. Soc. Math. France 84 (1956), 307–317. MR 86358, DOI 10.24033/bsmf.1475
- Hyman Bass, Algebraic $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0249491
- H. Bass, A. Heller, and R. G. Swan, The Whitehead group of a polynomial extension, Inst. Hautes Études Sci. Publ. Math. 22 (1964), 61–79. MR 174605, DOI 10.1007/BF02684690
- N. Bourbaki, Éléments de mathématique. 23. Première partie: Les structures fondamentales de l’analyse. Livre II: Algèbre. Chapitre 8: Modules et anneaux semi-simples, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1261, Hermann, Paris, 1958 (French). MR 0098114
- S. M. Gersten, Higher $K$-theory of rings, Algebraic $K$-theory, I: Higher $K$-theories (Proc. Conf. Seattle Res. Center, Battelle Memorial Inst., 1972) Lecture Notes in Math., Vol. 341, Springer, Berlin, 1973, pp. 3–42. MR 0382398
- Daniel Quillen, Higher algebraic $K$-theory. I, Algebraic $K$-theory, I: Higher $K$-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972) Lecture Notes in Math., Vol. 341, Springer, Berlin, 1973, pp. 85–147. MR 0338129
- Leslie G. Roberts, $K_{1}$ of some abelian categories, Trans. Amer. Math. Soc. 138 (1969), 377–382. MR 251109, DOI 10.1090/S0002-9947-1969-0251109-4
- Leslie G. Roberts, $K_{1}$ of projective $r$-spaces, Proc. Amer. Math. Soc. 26 (1970), 587–592. MR 280501, DOI 10.1090/S0002-9939-1970-0280501-0
- Leslie G. Roberts, Indecomposable vector bundles on the projective line, Canadian J. Math. 24 (1972), 149–154. MR 297776, DOI 10.4153/CJM-1972-013-9 —, Real quadrics and ${K_1}$ of a curve of genus zero, Mathematical Preprint No. 1971-60, Queen’s University at Kingston, Ont.
- Leslie Roberts, Base change for $K_{0}$ of algebraic varieties, Algebraic $K$-theory, II: “Classical” algebraic $K$-theory and connections with arithmetic (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972) Lecture Notes in Math., Vol. 342, Springer, Berlin, 1973, pp. 122–134. MR 0396577
- Winfried Scharlau, Quadratic forms, Queen’s Papers in Pure and Applied Mathematics, No. 22, Queen’s University, Kingston, Ont., 1969. MR 0269679
- Shianghaw Wang, On the commutator group of a simple algebra, Amer. J. Math. 72 (1950), 323–334. MR 34380, DOI 10.2307/2372036
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 188 (1974), 319-326
- MSC: Primary 14F05
- DOI: https://doi.org/10.1090/S0002-9947-1974-0332787-X
- MathSciNet review: 0332787