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Proceedings of the American Mathematical Society
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Simultaneous Surface Resolution in Cyclic Galois Extensions

Author(s): Shreeram S. Abhyankar; Nan Gu
Journal: Proc. Amer. Math. Soc. 136 (2008), 449-452.
MSC (2000): Primary 14A05
Posted: November 1, 2007
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Abstract | References | Similar articles | Additional information

Abstract: We show that simultaneous surface resolution is not always possible in a cyclic extension whose degree is greater than three and is not divisible by the characteristic. This answers a recent question of Ted Chinburg.


References:

[Ab1]
S. S. Abhyankar, On the valuations centered in a local domain, American Journal of Mathematics, 78 (1956), 321-348. MR 0082477 (18:556b)

[Ab2]
S. S. Abhyankar, Simultaneous resolution for algebraic surfaces, American Journal of Mathematics, 78 (1956), 761-790. MR 0082722 (18:600b)

[Ab3]
S. S. Abhyankar, Uniformization of Jungian local domains, Mathematische Annalen, 159 (1965), 1-43. MR 0177989 (31:2247)

[Ab4]
S. S. Abhyankar, Resolution of Singularities of Embedded Algebraic Surfaces, Springer Verlag (1998). MR 1617523 (99c:14021)

[Ab5]
S. S. Abhyankar, Lectures on Algebra I, World Scientific, 2006.

[AbK]
S. S. Abhyankar and M. Kumar, Simultaneous surface resolution in quadratic and biquadratic Galois extensions, Contemporary Mathematics, 390 (2005), 1-8. MR 2187320 (2006h:14017)

[Har]
D. Harbater, Fundamental groups and embedding problems in characteristic $ p$, Contemporary Mathematics, 186 (1995), 353-369. MR 1352282 (97b:14035)

[Pop]
F. Pop, Étale Galois covers of affine smooth curves, Invent. Math., 120 (1995), 555-578. MR 1334484 (96k:14011)

[Zar]
O. Zariski, The problem of minimal models in the theory of algebraic surfaces, American Journal of Mathematics, 80 (1958), 146-184. MR 0097404 (20:3873)

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Additional Information:

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

Nan Gu
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: ngu@math.purdue.edu

DOI: 10.1090/S0002-9939-07-09269-6
PII: S 0002-9939(07)09269-6
Received by editor(s): August 28, 2006
Received by editor(s) in revised form: November 9, 2006
Posted: November 1, 2007
Communicated by: Ted Chinburg
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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