×

\(K_2\) of discrete valuation rings. (English) Zbl 0318.13017


MSC:

13D15 Grothendieck groups, \(K\)-theory and commutative rings
13H99 Local rings and semilocal rings
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Alperin, R. C.; Dennis, R. K.; Stein, M. R., The non-triviality of \(SK_1\)(), (Lecture Notes in Mathematics, Vol. 353 (1973), Springer-Verlag: Springer-Verlag Berlin), 1-7
[2] Bass, H., \(K_2\) des corps globaux, Séminaire Bourbaki 1970/1971, No. 394, (Lecture Notes in Mathematics, Vol. 244 (1971), Springer-Verlag: Springer-Verlag Berlin)
[3] Bass, H.; Milnor, J.; Serre, J.-P, Solution of the congruence subgroup problem for \(SL_n(n\) ⩾ 3) and \(Sp_{2n}(n\) ⩾ 2), Publ. Math. IHES, No. 33, 59-137 (1967) · Zbl 0174.05203
[4] Borel, A., Linear Algebraic Groups (1969), W. A. Benjamin: W. A. Benjamin New York · Zbl 0186.33201
[5] Christofides, A., Structure and Presentations of Unimodular Groups, (Thesis (1966), Queen Mary College, University of London)
[6] Cohen, I. S., On the structure and ideal theory of complete local rings, Trans. Amer. Math. Soc., 59, 54-106 (1946) · Zbl 0060.07001
[7] Cohn, P. M., On the structure of the \(GL_2\) of a ring, Publ. Math. IHES, No. 30, 5-53 (1966)
[8] Dennis, R. K., Stability for \(K_2\), (Lecture Notes in Mathematics, Vol. 353 (1973), Springer-Verlag: Springer-Verlag Berlin), 85-94
[9] Dennis, R. K.; Stein, M. R., A new exact sequence for \(K_2\) and some consequences for rings of integers, Bull. Amer. Math. Soc., 78, 600-603 (1972) · Zbl 0261.18012
[10] Gersten, S. M., Some exact sequences in the higher \(K\)-theory of rings, (Lecture Notes in Mathematics, Vol. 341 (1973), Springer-Verlag: Springer-Verlag Berlin), 211-243 · Zbl 0289.18011
[11] Graham, J. N., Continuous symbols on fields of formal power series, (Lecture Notes in Mathematics, Vol. 342 (1973), Springer-Verlag: Springer-Verlag Berlin), 474-486
[12] Hasse, H., Zahlentheorie (1963), Akademie-Verlag: Akademie-Verlag Berlin · Zbl 0035.02002
[13] Kaplansky, I., Infinite Abelian Groups (1969), University of Michigan Press: University of Michigan Press Ann Arbor · Zbl 0194.04402
[14] Magnus, W.; Karass, A.; Solitar, D., Combinatorial Group Theory (1966), Wiley-Interscience: Wiley-Interscience New York
[15] Matsumoto, H., Sur les sous-groupes arithmétiques des groupes semi-simples déployés, Ann. Sci. École Norm. Sup., 2, 4, 1-62 (1969) · Zbl 0261.20025
[16] Milnor, J., Introduction to Algebraic \(K\)-Theory, (Annals of Math. Studies Number 72 (1971), Princeton University Press: Princeton University Press Princeton) · Zbl 0237.18005
[17] Moore, C., Group extensions of \(p\)-adic and adelic linear groups, Publ. Math. IHES, No. 35, 5-70 (1968) · Zbl 0159.03203
[18] Math. Notes, 840-845 (1972), New York · Zbl 0238.12010
[19] Quillen, D., Higher algebraic \(K\)-theory: I, (Lecture Notes in Mathematics, Vol. 341 (1973), Springer-Verlag: Springer-Verlag Berlin), 85-147 · Zbl 0292.18004
[20] Serre, J.-P, Corps Locaux (1962), Hermann: Hermann Paris · Zbl 0137.02601
[21] Silvester, J. R., On the \(K_2\) of a free associative algebra, (Proc. London Math. Soc. (3), 26 (1973)), 35-56 · Zbl 0249.18023
[22] Stein, M. R., Generators, relations and coverings of Chevalley groups over commutative rings, Amer. J. Math., 93, 965-1004 (1971) · Zbl 0246.20034
[23] Stein, M. R., Surjective stability in dimension 0 for \(K_2\) and related functors, Trans. Amer. Math. Soc., 178, 165-191 (1973) · Zbl 0267.18015
[24] Stein, M. R.; Dennis, R. K., \(K_2\) of radical ideals and semi-local rings revisited, (Lecture Notes in Mathematics, Vol. 342 (1973), Springer-Verlag: Springer-Verlag Berlin), 281-303
[25] Steinberg, R., Générateurs, rélations et revêtements de groupes algébriques, (Colloq. Théorie des Groupes Algébriques. Colloq. Théorie des Groupes Algébriques, Bruxelles, 1962 (1962), Librairie Universitaire, Louvain, Gauthier-Villars: Librairie Universitaire, Louvain, Gauthier-Villars Paris), 113-127 · Zbl 0272.20036
[26] Swan, R. G., Excision in algebraic \(K\)-theory, J. Pure Appl. Algebra, 1, 221-252 (1971) · Zbl 0262.16025
[27] Tate, J., Symbols in arithmetic, (Actes du Congrès International des Mathématiciens 1970, Tome 1 (1971), Gauthier-Villars: Gauthier-Villars Paris), 201-211
[28] van der Kallen, W., Le \(K_2\) des nombres duaux, C. R. Acad. Sci. Paris, 273, 1204-1207 (20 décembre 1971), Ser. A-B
[29] Weiss, E., Algebraic Number Theory (1963), McGraw-Hill: McGraw-Hill New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.