Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

Local fundamental groups of algebraic varieties

Author(s): Shreeram S. Abhyankar
Journal: Proc. Amer. Math. Soc. 125 (1997), 1635-1641.
MSC (1991): Primary 12F10, 14H30, 20D06, 20E22
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: Some progress is made in the calculation of local fundamental groups.


References:

[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


Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 12F10, 14H30, 20D06, 20E22

Retrieve articles in all Journals with MSC (1991): 12F10, 14H30, 20D06, 20E22


Additional Information:

Shreeram S. Abhyankar
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: ram@cs.purdue.edu

DOI: 10.1090/S0002-9939-97-03938-5
PII: S 0002-9939(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
Copyright of article: Copyright 1997, American Mathematical Society


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google