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Local fundamental groups of algebraic varieties


Author: Shreeram S. Abhyankar
Journal: Proc. Amer. Math. Soc. 125 (1997), 1635-1641
MSC (1991): Primary 12F10, 14H30, 20D06, 20E22
DOI: https://doi.org/10.1090/S0002-9939-97-03938-5
MathSciNet review: 1403110
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Abstract: Some progress is made in the calculation of local fundamental groups.


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  • [1] S. S. Abhyankar, On the ramification of algebraic functions, American Journal of Mathematics 77 (1955), 572-592. MR 17:193c
  • [2] S. S. Abhyankar, Local uniformization on algebraic surfaces over ground fields of characteristic $p\ne 0$, Annals of Mathematics 63 (1956), 491-526. MR 17:1134d
  • [3] S. S. Abhyankar, Coverings of algebraic curves, American Journal of Mathematics 79 (1957), 825-856. MR 20:872
  • [4] S. S. Abhyankar, On the ramification of algebraic functions Part II, Transactions of the American Mathematical Society 89 (1958), 310-324. MR 20:5204
  • [5] S. S. Abhyankar, Tame coverings and fundamental groups of algebraic varieties Parts I to VI, American Journal of Mathematics 81-82 (1959-1960), 46-94 of vol 81 and 120-190 + 341-388 of vol 82. MR 22:1578; MR 21:3428
  • [6] S. S. Abhyankar, Resolution of singularities of arithmetical surfaces, Arithmetical Algebraic Geometry (1965), 111-152. MR 34:171
  • [7] S. S. Abhyankar, Resolution of Singularities of Embedded Algebraic Surfaces, Academic Press, 1966. MR 36:164
  • [8] S. S. Abhyankar, Galois theory on the line in nonzero characteristic, Bulletin of the American Mathematical Society 27 (1992), 68-133. MR 94a:12004
  • [9] S. S. Abhyankar, Nice equations for nice groups, Israel Journal of Mathematics 88 (1994), 1-24. MR 96f:12003
  • [10] S. S. Abhyankar, Mathieu group coverings and linear group coverings, Contemporary Mathematics 186 (1995), 293-319. CMP 96:01
  • [11] S. S. Abhyankar, Projective polynomials (To Appear).
  • [12] R. Dedekind and H. Weber, Theorie der alg. Funktionen einer veränderlichen, Crelle Journal 92 (1882), 181-290.
  • [13] D. Harbater, Abhyankar's conjecture on Galois groups over curves, Inventiones Mathematicae 117 (1994), 1-25. MR 95i:14029
  • [14] H. W. E. Jung, Darstellung der Funktionen eines algebraischen Körpers zweier Veränderlichen $x,y$ in der Umgebung einer Stelle $x=a,y=b$, Crelle Journal 133 (1908), 289-314.
  • [15] M. Nagata, On the purity of branch loci in regular local rings, Illinois Journal of Mathematics 3 (1959), 328-333. MR 21:5660
  • [16] M. Noether, Über die alg. Functionen einer und zweier Variabeln, Göttinger Nachrichten (1871).
  • [17] M. Raynaud, Revêtment de la droit affine en charactéristic $p>0$ et conjecture d'Abhyankar, Inventiones Mathematicae 116 (1994), 425-462. MR 94m:14034
  • [18] B. Riemann, Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse, Inauguraldissertation, Göttingen (1851), 1-48.
  • [19] K. F. Stevenson, Galois groups of unramified covers of projective curves in characteristic $p$, Journal of Algebra 44, (To Appear).
  • [20] O. Zariski, On the purity of the branch locus of algebraic functions, Proc. Nat. Acad. Sci. U.S.A. 44 (1958), 791-796. MR 20:2344

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Additional Information

Shreeram S. Abhyankar
Email: ram@cs.purdue.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03938-5
Received by editor(s): January 5, 1996
Additional Notes: This work was partly supported by NSF grant DMS 91–01424 and NSA grant MDA 904–92–H–3035.
Dedicated: Dedicated to Walter Feit for his Sixty-Fifth Birthday
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society

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