Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
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)

     

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
MathSciNet review: 2358482
Retrieve article in: PDF

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)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14A05

Retrieve articles in all Journals with MSC (2000): 14A05


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.




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia