×

Vector bundles over affine surfaces. (English) Zbl 0362.14006


MSC:

14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry
13D15 Grothendieck groups, \(K\)-theory and commutative rings
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14J99 Surfaces and higher-dimensional varieties
PDF BibTeX XML Cite
Full Text: DOI EuDML

References:

[1] Abhyankar, S.S.: Resolution of singularities of embedded algebraic surfaces. New York: Academic Press 1966 · Zbl 0147.20504
[2] Andreotti, A., Frankel, T.: The Lefschetz theorem of hyperplane sections. Ann. of Math.69, 713-717 (1959) · Zbl 0115.38405
[3] Artin, M., Bloch, L., Kas, A., Lieberman, D.: Zero cycles on surfaces withp g =0. To appear
[4] Barsotti, I.: Structure theorems for group varieties. Ann. di Mat.38, 77-119 (1955) · Zbl 0068.34301
[5] Bass, H.: AlgebraicK-theory. New York: Benjamin 1968 · Zbl 0174.30302
[6] Bass, H.: Libération des modules projectifs sur certains anneaux de polynômes. Sem. Bourb. 26{\(\deg\)} an. 1973/74 no 448
[7] Bloch, S.:K 2 of artinianQ-algebras with application to algebraic cycles. To appear
[8] Bombieri, E.: The pluricanonical map of a complex surface. Several complex variables. Maryland 1970, p. 35-87. Lecture Notes in Mathematics155. Berlin-Heidelberg-New York: Sprigner 1970 · Zbl 0213.47601
[9] Borel, A.: Linear algebraic groups. New York: Benjamin 1969 · Zbl 0206.49801
[10] Borel, S., Serre, J.-P.: Groupes de Lie et puissances reduit de Steenrod. Am. J. Math.75, 409-448 (1953) · Zbl 0050.39603
[11] Borel, A., Serre, J.-P.: Le théorème de Riemann-Roch. Bull. Soc. Math. (France)86, 97-136 (1958) · Zbl 0091.33004
[12] Bott, R.: The space of loops on a Lie group. Mich. Math. J.5, 35-61 (1958) · Zbl 0096.17701
[13] Eagon, J.: The Grothendieck group of finitely generated modules. Proc. Amer. Math. Soc.19, 1341-1345 (1968) · Zbl 0167.31202
[14] Eklof, P.: Lefschetz’s principle and local functors. Proc. Amer. Math. Soc.37, 333-339 (1973) · Zbl 0254.14004
[15] Fulton, W.: Rational equivalence on singular varieties. To appear · Zbl 0332.14002
[16] Goldman, O.: Determinants in projective modules. Nagoya Math. J.18, 27-36 (1961) · Zbl 0103.27001
[17] Goodman, J.E.: Affine open subsets of algebraic varieties and ample divisors. Ann. of Math.89, 160-183 (1969) · Zbl 0167.19301
[18] Grauert, H.: Analytische Faserungen über holomorphvollständigen Räumen. Math. Ann.135, 263-273 (1958) · Zbl 0081.07401
[19] Grothendieck, A.: La théorie des classes de Chern. Bull. Soc. Math. (France)86, 137-154 (1958) · Zbl 0091.33201
[20] Grothendieck, A.: Revêtements etales et groupe fondamental (SGAI) Lect. Notes in Math. 224. Berlin-Heidelberg-New York: Springer Verlag 1971
[21] Grothendieck, A., Berthelot, P., Illusie, L., et al.: Théorie des intersections et thèorème de Riemann-Roch (SGA6). Lect. Notes in Math.225. Berlin-Heidelberg-New York: Springer 1971 · Zbl 0218.14001
[22] Gunning, R., Rossi, H.: Analytic functions of several complex variables. Prentice Hall Englewood Cliffs, New Jersey 1965 · Zbl 0141.08601
[23] Hartshorne, R.: Ample Subvarieties of Algebraic Varieties, Lecture Notes in Mathematics156. Berlin-Heidelberg-New York: Springer 1970 · Zbl 0208.48901
[24] Hartshorne, R.: Equivalence Relations on Algebraic Cycles, Lecture Notes, Summer Inst. on Alg. Geom. at Humboldt State Univ. Amer. Math. Soc. 1974 · Zbl 0288.14006
[25] Hu, S. T.: Homotopy Theory, New York: Academic Press 1959 · Zbl 0088.38803
[26] Kaplansky, I.: Commutative Rings, Boston: Allyn and Bacon 1970 · Zbl 0203.34601
[27] Kaplansky, I.: Fields and rings. Chicago 1969 · Zbl 0184.24201
[28] Lang, S.: On quasi algebraic closure. Ann. of Math.55, 373-390 (1952) · Zbl 0046.26202
[29] Lang, S.: Diophantine geometry, New York: Interscience 1962 · Zbl 0115.38701
[30] Lang, S.: Abelian varieties. New York: Interscience 1959 · Zbl 0099.16103
[31] Lech, C.: A note on recurring series. Ark. Math.2, 417-421 (1953) · Zbl 0051.27801
[32] Lutz, E.: Sur l’équationy 2=x 3?Ax?B dans les corpsp-adiques. J. Math.177, 238-247 (1937) · JFM 63.0101.01
[33] Milnor, J.: Construction of universal bundles II. Ann. of Math.63, 430-436 (1956) · Zbl 0071.17401
[34] Milnor, J.: Morse theory. Ann. Math. Studies 51, Princeton 1963 · Zbl 0108.10401
[35] Mumford, D.: Abelian varieties, Oxford 1970 · Zbl 0223.14022
[36] Mumford, D.: Rational equivalence of 0-cycles on surfaces. J. Math. Kyoto Univ.9, 195-204 (1969) · Zbl 0184.46603
[37] Mumford, D.: The topology of normal singularities of an algebraic surface and a criterion for simplicity. Publ. Math. I.H.E.S.9, 5-22 (1961) · Zbl 0108.16801
[38] Murthy, M.P.: Vector bundles over affine surfaces birationally equivalent to a ruled surface. Ann. of Math.89, 242-253 (1969) · Zbl 0185.24504
[39] Narasimhan, R.: On the homology groups of Stein spaces. Inv. Math.2, 377-385 (1967) · Zbl 0148.32202
[40] Raynaud, M.: Modules projectifs universels. Inv. Math.6, 1-26 (1968) · Zbl 0216.32601
[41] Roitman, A.A.: On ?-equivalence of zero-dimensional cycles. Math. USSR Sbornik15, 555-567 (1971) · Zbl 0259.14002
[42] Roitman, A.A.: Rational equivalence of zero-cycles. Math. USSR Sbornik18, 571-588 (1972) · Zbl 0273.14001
[43] Roitman, A.A.: Ruledness of an algebraic surface with a finite-dimensional non-zero group of classes of zero-dimensional cycles of degree zero modulo rational equivalence. Func. Anal. and Appl.8, 82-83 (1974) · Zbl 0337.14027
[44] Rosenlicht, M.: Some basic theorems on algebraic groups. Am. J. Math.78, 401-443 (1956) · Zbl 0073.37601
[45] ?afarevi?, J.: Algebraic surfaces. Proc. Steklov Inst. Math. 75 (1965) · Zbl 0154.21001
[46] ?afarevi?, J.: Lectures on minimal models and birational transformations of two-dimensional schemes. Bombay: Tata Institute 1966
[47] Schwarzenberger, R.: Vector bundles on the projective plane. Proc. London Math. Soc.11, 623-640 (1961) · Zbl 0212.26004
[48] Serre, J.P.: Homologie singulière des espaces fibres. Applications. Ann. of Math.54, 425-505 (1951) · Zbl 0045.26003
[49] Serre, J-P.: Groupes d’homotopie et classes de groupes abéliens. Ann of Math.58, 258-294 (1953) · Zbl 0052.19303
[50] Serre, J-P.: Faisceaux algébriques cohérents. Ann. of Math.61, 197-278 (1955) · Zbl 0067.16201
[51] Serre, J-P.: Algèbre locale-multiplicités. Lect. Notes in Math.11. Berlin-Heidelberg-New York: Springer 1965
[52] Serre, J-P.: Corps locaux. Paris: Hermann 1962 · Zbl 0137.02601
[53] Serre, J-P.: Groups algébriques et corps classes. Paris: Hermann 1959
[54] Serre, J-P.: Modules projectifs et espaces fibres à fibre vectorielle. Sem. Dubreil-Pisot 11. Paris 1957/8
[55] Serre, J.-P.: Sur les modules projectifs. Sem. Dubreil-Pisot 14 (1960-(61), No.2
[56] Serre, J-P.: Classes des corps cyclotomique, Sem. Bourbaki 174 (1958)
[57] Swan, R.G.: Vector bundles and projective modules. Trans. Amer. Math. Soc.105, 264-277 (1962) · Zbl 0109.41601
[58] Swan, R.G.: AlgebraicK-theory. Lect. Notes in Math.76 Berlin-Heidelberg-New York: Springer 1968 · Zbl 0193.34601
[59] Swan, R.G.:K-Theory of finite groups and orders. Notes. by E. G. Evans. Lecture Notes in Mathematics 149. Berlin-Heidelberg-New York Springer 1970 · Zbl 0205.32105
[60] Swan, R. G.: A cancellation theorem for projective modules in the metastable range. Inventiones math.27, 23-43 (1974) · Zbl 0297.14003
[61] Swan, R.G., Towber, J.: A class of projective modules which are nearly free. J. Alg.36, 427-434 (1975) · Zbl 0322.13009
[62] Tsen, C.: Divisionalgebren über Funktionenkörper. Nachr. Ges. Wiss. Göttingen 1933, 335-7 (1975)
[63] Weil, A.: Foundations of algebraic geometry. Amer. Math. Soc. Colloq. Publ. XXIX, Providence 1962 · Zbl 0168.18701
[64] Zariski, O.: Algebraic surfaces. Berlin-Heidelberg-New York: Springer 1971 · Zbl 0219.14020
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.