Simultaneous Surface Resolution in Cyclic Galois Extensions
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- by Shreeram S. Abhyankar and Nan Gu
- Proc. Amer. Math. Soc. 136 (2008), 449-452
- DOI: https://doi.org/10.1090/S0002-9939-07-09269-6
- Published electronically: November 1, 2007
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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
- Shreeram Abhyankar, On the valuations centered in a local domain, Amer. J. Math. 78 (1956), 321–348. MR 82477, DOI 10.2307/2372519
- Shreeram Abhyankar, Simultaneous resolution for algebraic surfaces, Amer. J. Math. 78 (1956), 761–790. MR 82722, DOI 10.2307/2372467
- Shreeram Abhyankar, Uniformization of Jungian local domains, Math. Ann. 159 (1965), 1–43. MR 177989, DOI 10.1007/BF01359903
- S. S. Abhyankar, Resolution of singularities of embedded algebraic surfaces, 2nd ed., Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1998. MR 1617523, DOI 10.1007/978-3-662-03580-1
- S. S. Abhyankar, Lectures on Algebra I, World Scientific, 2006.
- Shreeram S. Abhyankar and Manish Kumar, Simultaneous surface resolution in quadratic and biquadratic Galois extensions, Commutative algebra and algebraic geometry, Contemp. Math., vol. 390, Amer. Math. Soc., Providence, RI, 2005, pp. 1–8. MR 2187320, DOI 10.1090/conm/390/07289
- David Harbater, Fundamental groups and embedding problems in characteristic $p$, Recent developments in the inverse Galois problem (Seattle, WA, 1993) Contemp. Math., vol. 186, Amer. Math. Soc., Providence, RI, 1995, pp. 353–369. MR 1352282, DOI 10.1090/conm/186/02191
- Florian Pop, Étale Galois covers of affine smooth curves. The geometric case of a conjecture of Shafarevich. On Abhyankar’s conjecture, Invent. Math. 120 (1995), no. 3, 555–578. MR 1334484, DOI 10.1007/BF01241142
- Oscar Zariski, The problem of minimal models in the theory of algebraic surfaces, Amer. J. Math. 80 (1958), 146–184. MR 97404, DOI 10.2307/2372827
Bibliographic 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
- Received by editor(s): August 28, 2006
- Received by editor(s) in revised form: November 9, 2006
- Published electronically: November 1, 2007
- Communicated by: Ted Chinburg
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 449-452
- MSC (2000): Primary 14A05
- DOI: https://doi.org/10.1090/S0002-9939-07-09269-6
- MathSciNet review: 2358482