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Serre’s problem on projective modules over polynomial rings and algebraic K-theory. (English. Russian original) Zbl 0293.13007

Funct. Anal. Appl. 8, 148-150 (1974); translation from Funkts. Anal. Prilozh. 8, No. 2, 65-66 (1974).

MSC:

13D15 Grothendieck groups, \(K\)-theory and commutative rings
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
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References:

[1] J.-P. Serre, ”Faisceaux alg?briques coh?rents,” Ann. Math.,61, 197-278 (1955). · Zbl 0067.16201
[2] H. Bass, ”Modules which support nonsingular forms,” J. Algebra,13, 246-252 (1969). · Zbl 0179.05401
[3] H. Bass, Algebraic K-Theory, Benjamin, New York (1968).
[4] V. A. Artamonov, ”Projective metabelian Lie algebras of finite rank,” Izv. Akad. Nauk SSSR, Ser. Matem.,36, No. 3, 510-522 (1972).
[5] M. Krusemeyer, ”Fundamental groups, algebraic K-theory, and a problem of Abhyankar,” Inv. Math.,19, 15-47 (1973). · Zbl 0247.14005
[6] H. Bass, Lecture Notes in Math., No. 342, Springer-Verlag, Berlin-Heidelberg-New York (1973), pp. 3-73.
[7] C. S. Seshadri, ”Triviality of vector bundles over the affine space K2,” Proc. Nat. Acad. Sci. USA,44, 456-458 (1958). · Zbl 0081.26603
[8] L. N. Vasershtein, ”The group SL2 over Dedekind rings of arithmetic type,” Matem. Sb.,89, No. 2, 313-322 (1972).
[9] M. Karoubi, Compt. Rend. Acad. Sci. Paris,273, A802-805 (1971) [see also Lecture Notes in Math., No. 343, Springer-Verlag, Berlin?Heidelberg?New York (1973), pp. 301-411].
[10] B. Segre, ”Intersezioni complete di due ipersuperficie algebriche in uno spazio affine, e non estendiblita di Seshadri,” Revue Roumaine de Math.,15, 1527-1534 (1970). · Zbl 0216.33201
[11] H. Bass, J. Milnor, and J.-P. Serre, ”Solution of the congruence subgroup problem for SLn (n ? 3) and Sp2n (n ? 2),” Publ. Math.,33, 59-137 (1967). · Zbl 0174.05203
[12] L. N. Vasershtein, ”Stabilization of unitary and orthogonal groups over a ring with involution,” Matem. Sb.,81, No. 3, 328-351 (1970).
[13] L. N. Vasershtein, ”Stable rank of rings and dimensionality of topological spaces,” Funktsional. Analiz i Ego Prilozhen.,5, No. 2, 17-27 (1971).
[14] H. Bass and J. Tate, Lecture Notes in Math., No. 342, Springer-Verlag, Berlin?Heidelberg?New York (1973), pp. 349-446.
[15] A. A. Suslin, The 12th All-Union Algebraic Colloquium [in Russian], Abstracts of Reports, Sverdlovsk (September 1973).
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