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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

The Jacobian conjecture: Reduction of degree and formal expansion of the inverse

Author(s): Hyman Bass; Edwin H. Connell; David Wright
Journal: Bull. Amer. Math. Soc. 7 (1982), 287-330.
MSC (1980): Primary 13B25, 13B10, 13B15, 14E05, 14E07; Secondary 05C05
MathSciNet review: 663785
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References:

[A + K] A. Altman and S. Kleiman, Introduction to Grothendieck duality, Lecture Notes in Math., vol. 146, Springer-Verlag, Berlin and New York, 1970. MR 274461

[Abl] S. S. Abhyankar, Expansion techniques in algebraic geometry, Tata Inst. Fundamental Research, Bombay, 1977. MR 542446

[Ab2] S. S. Abhyankar, Lectures in algebraic geometry, Notes by Chris Christensen, Purdue Univ., 1974.

[Ab3] S. S. Abhyankar, Historical ramblings in algebraic geometry and related algebra, Amer. Math. Monthly 83 (1976), 409-448. MR 401754

[A + H + E] S. S. Abhyankar, W. Heinzer and P. Eakin, On the uniqueness of the coefficient ring in a polynomial ring, J. Algebra 23 (1972), 310-342. MR 306173

[A + M] S. S. Abhyankar and T.-T. Moh, Embeddings of the line in the plane, J. Reine Angew. Math. 276 (1975), 149-166. MR 379502

[B] H. Bass, Algebraic K-theory, Benjamin, New York, 1968. MR 249491

[B + M) S. Bochner and W. T. Martin, Several complex variables, Princeton Univ. Press, Princeton, N. J., 1948. MR 27863

[C] L. A. Campbell, A condition for a polynomial map to be invertible, Math. Ann. 205 (1973), 243-248. MR 324062

[C + L] I. Canals and E. Lluis, Acerca de un resultado de Segre, Anal. Inst. Matematicas, Univ. Nacional Autonoma de Mexico 10 (1970), 1-15. MR 286794

[Co] E. H. Connell, A K-theory for the category of projective algebras, J. Pure Appl. Algebra 5 (1974), 281-292. MR 384803

[E] W. Engel, Ein Satz über ganze Cremona Transformationen der Ebene, Math. Ann. 130 (1955), 11-19. MR 75666

[F] L. Fridman, On a characterization of polynomial endomorphisms of C, Math. USSR Izv. 7 (1973), 319-328. (Transi, from Izv, Akad. Nauk SSR 37 (1973).) MR 332740

[Fu] T. Fujita, On Zariski problem, Proc. Japan Acad. 55 (1979), 106-110. MR 531454

[G] I. J. Good, Generalization to several variables of Lagrange's expansion, with applications to stochastic processes, Proc. Cambridge Philos. Soc. 56 (1960), 367-380. MR 123021

[Gr] W. Gröbner, Sopra un teorema di B. Segre, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. 31 (1961), 118-122. MR 24 (1962) A3155 (I. Barsotti). MR 133321

[J] C. G. J. Jacobi, De resolutione aequationum per series infinitas, J. Reine Angew. Math. 6 (1830), 257-286.

[Ja] A. V. Jagžev, On Keller's problem, Siberian Math. J. 21 (1980), 141-150. (Russian) MR 592226

[Jo] S. A. Joni, Lagrange inversion in higher dimension and umbral operators, Linear and Multilinear Algebra 6 ( 1978), 111 -121. MR 491220

[Ju] H. W. E. Jung, Über ganze birationale Transformation der Ebene, J. Reine Angew. Math. 184 (1942), 161-174. MR 8915

[K] O. H. Keller, Ganze Cremona-Transformationen, Monats. Math. Physik 47 (1939), 299-306. MR 1550818

[Ma] A. Magnus, On polynomial solutions of a differential equation, Math. Scand. 3 (1955), 255-260. MR 78453

[M-L] G. Makar-Limanov, Automorphisms of a free algebra on two generators, Functional Anal. Appl. 4 (1970), 262-264 (Transl. from Funkcional Anal. i. Prilozen 4 (1970), 107-108.) MR 271161

[Mat] H. Matsumura, Commutative algebra, Benjamin, New York, 1970. MR 266911

[Me] Gary H. Meisters, Jacobian problems in differential equations and algebraic geometry, Rocky Mountain J. Math, (to appear). MR 683862

[Mo] T.-T. Moh, On the Jacobian Conjecture and the configuration of roots, J. Reine Angew. Math, (to appear). MR 691964

[Mu] J. P. Murre, An introduction to Grothendieck's theory of the fundamental group, Tata Inst. Fundamental Research, Bombay, 1967. MR 302650

[N + B] Y. Nakai and K. Baba, A generalization of Magnus' theorem, Osaka J. Math. 14 (1977), 403-409. MR 485879

[N1] Pekka Nousiainen, On the Jacobian problem in positive characteristic, Pennsylvania State Univ., preprint, 1981. MR 648679

[N2] Pekka Nousiainen, On the degrees of smooth maps of affine space, Pennsylvania State Univ., preprint, 1981.

[N + S] P. Nousiainen and M. Sweedler, Automorphisms of polynomial and power series rings, Cornell Univ., preprint, 1981. MR 704289

[O] Susumu Oda, The Jacobian problem and the simply-connectedness of A, Osaka Univ., preprint, 1980.

[R] M. Razar, Polynomial maps with constant Jacobian, Israel J. Math. 32 (1979), 97-106. MR 531253

[S] I. R. Shafarevich, On some infinite dimensional groups, Simposio Internazionale di Geometria Algebrica, 1965, published in Rendiconti di Matematica e delle sue applicazioni, Ser. 5, vol. 25, 1966, pp. 208-2121. MR 485898

[Se1] B. Segre, Corrispondenze di Mobius e Transformazioni cremoniane intere, Atti della Accademia delle Scienze di Torino, Classe di Scienzo Fisiche, Mat. e Natural. 91 (1956-57), 3-19. MR 95175

[Se2]B. Segre, Forme differenziali e loro integrali, vol. II, Docet, Roma, 1956.

[Se3] B. Segre, Variazione continua ed omotopia in geometria algebrica, Ann. Math. Pura Appl. 100 (1960), 149-186. MR 121698

[V] A. G. Vitushkin, On polynomial transformation of C (Tokyo, 1973), Tokyo Univ. Press, Tokyo, 1975, pp. 415-417. MR 369367

[Wa] S. Wang, A jacobian criterion for separability, J. Algebra 65 ( 1980), 453-494. MR 585736

[Wr1] D. Wright, The amalgamated free product structure of GL, J. Pure and Appl. Algebra 12 (1978), 235-251. MR 501951

[Wr2] D. Wright, On the Jacobian Conjecture, Illinois J. Math. 25 (1981), 423-440. MR 620428


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Additional Information:

DOI: 10.1090/S0273-0979-1982-15032-7
PII: S 0273-0979(1982)15032-7




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