Galois covers of 1 over with prescribed local or global behavior by specialization

Bernat Plans[1]; Núria Vila[2]

  • [1] Dept. de Matemàtica Aplicada I Universitat Politècnica de Catalunya Av. Diagonal, 647 08028 Barcelona, Spain
  • [2] Dept. d’Àlgebra i Geometria Universitat de Barcelona Gran Via de les Corts Catalanes, 585 08007 Barcelona, Spain

Journal de Théorie des Nombres de Bordeaux (2005)

  • Volume: 17, Issue: 1, page 271-282
  • ISSN: 1246-7405

Abstract

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This paper considers some refined versions of the Inverse Galois Problem. We study the local or global behavior of rational specializations of some finite Galois covers of 1 .

How to cite

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Plans, Bernat, and Vila, Núria. "Galois covers of $\mathbb{P}^1$ over $\mathbb{Q}$ with prescribed local or global behavior by specialization." Journal de Théorie des Nombres de Bordeaux 17.1 (2005): 271-282. <http://eudml.org/doc/249432>.

@article{Plans2005,
abstract = {This paper considers some refined versions of the Inverse Galois Problem. We study the local or global behavior of rational specializations of some finite Galois covers of $\mathbb\{P\}^1_\mathbb\{Q\}$.},
affiliation = {Dept. de Matemàtica Aplicada I Universitat Politècnica de Catalunya Av. Diagonal, 647 08028 Barcelona, Spain; Dept. d’Àlgebra i Geometria Universitat de Barcelona Gran Via de les Corts Catalanes, 585 08007 Barcelona, Spain},
author = {Plans, Bernat, Vila, Núria},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {inverse Galois problem; Galois covers of },
language = {eng},
number = {1},
pages = {271-282},
publisher = {Université Bordeaux 1},
title = {Galois covers of $\mathbb\{P\}^1$ over $\mathbb\{Q\}$ with prescribed local or global behavior by specialization},
url = {http://eudml.org/doc/249432},
volume = {17},
year = {2005},
}

TY - JOUR
AU - Plans, Bernat
AU - Vila, Núria
TI - Galois covers of $\mathbb{P}^1$ over $\mathbb{Q}$ with prescribed local or global behavior by specialization
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 1
SP - 271
EP - 282
AB - This paper considers some refined versions of the Inverse Galois Problem. We study the local or global behavior of rational specializations of some finite Galois covers of $\mathbb{P}^1_\mathbb{Q}$.
LA - eng
KW - inverse Galois problem; Galois covers of
UR - http://eudml.org/doc/249432
ER -

References

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  1. J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson, Atlas of Finite Groups. New York: Clarendon press, 1985. Zbl0568.20001MR827219
  2. S. Beckmann, On extensions of number fields obtained by specializing branched coverings. J. Reine Angew. Math. 419 (1991), 27–53. Zbl0721.11052MR1116916
  3. S. Beckmann, Is every extension of the specialization of a branched covering? J. Algebra 165 (1994), 430–451. Zbl0802.12003MR1271246
  4. B. Birch, Noncongruence subgroups, Covers and Drawings. Leila Schneps, editor, The Grothendieck theory of dessins d’enfants. Cambridge Univ. Press (1994), 25–46. Zbl0930.11024MR1305392
  5. E. Black, Deformations of dihedral 2-group extensions of fields. Trans. Amer. Math. Soc. 351 (1999), 3229–3241. Zbl0931.12005MR1467461
  6. E. Black, On semidirect products and the arithmetic lifting property. J. London Math. Soc. (2) 60 (1999), 677–688. Zbl0944.12001MR1753807
  7. J.-L. Colliot-Thélène, Rational connectedness and Galois covers of the projective line. Ann. of Math. 151 (2000), 359–373. Zbl0990.12003MR1745009
  8. P. Dèbes, Some arithmetic properties of algebraic covers. H. Völklein, D. Harbater, P. Müller, and J. G. Thompson, editors, Aspects of Galois theory. London Math. Soc. LNS 256 (2). Cambridge Univ. Press (1999), 66–84. Zbl0977.14009MR1708602
  9. P. Dèbes, Galois Covers with Prescribed Fibers: the Beckmann-Black Problem. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28 (1999), 273–286. Zbl0954.12002MR1736229
  10. P. Dèbes, Density results for Hilbert subsets. Indian J. pure appl. Math. 30 (1) (1999), 109–127. Zbl0923.12001MR1677959
  11. C. U. Jensen, A. Ledet, N. Yui, Generic polynomials. Cambridge Univ. Press, Cambridge, 2002. Zbl1042.12001MR1969648
  12. J. Klüners, G. Malle, A database for field extensions of the rationals. LMS J. Comput. Math. 4 (2001), 182–196. Zbl1067.11516MR1901356
  13. J. Klüners, G. Malle, Counting nilpotent Galois extensions. J. reine angew. Math. 572 (2004), 1–26. Zbl1052.11075MR2076117
  14. G. Malle, B. H. Matzat, Inverse Galois Theory. Springer, Berlin, 1999. Zbl0940.12001MR1711577
  15. J.-F. Mestre, Extensions régulières de ( T ) de groupe de Galois A ˜ n . J. Algebra 131 (1990), 483–495. Zbl0714.11074MR1058560
  16. J.-F. Mestre, Relèvement d’extensions de groupe de Galois PSL 2 ( 𝔽 7 ) . Preprint (2004), arXiv:math.GR/0402187. 
  17. J. Montes, E. Nart, On a Theorem of Ore. J. Algebra 146 (1992), 318–334. Zbl0762.11045MR1152908
  18. L. Moret-Bailly, Construction de revêtements de courbes pointées. J. Algebra 240 (2001), 505–534. Zbl1047.14013MR1841345
  19. Y. Morita, A Note on the Hilbert Irreducibility Theorem. Japan Acad. Ser. A Math. Sci. 66 (1990), 101–104. Zbl0725.12003MR1065782
  20. Ö. Ore, Newtonsche Polygone in der Theorie der algebraischen Körper. Math. Ann. 99 (1928), 84–117. Zbl54.0191.02MR1512440
  21. B. Plans, Central embedding problems, the arithmetic lifting property and tame extensions of . Internat. Math. Res. Notices 2003 (23) (2003), 1249–1267. Zbl1044.12004MR1967317
  22. B. Plans, N. Vila, Tame A n -extensions of . J. Algebra 266 (2003), 27–33. Zbl1057.12003MR1994526
  23. B. Plans, N. Vila, Trinomial extensions of with ramification conditions. J. Number Theory 105 (2004), 387–400. Zbl1048.11086MR2040165
  24. D. Saltman, Generic Galois extensions and problems in field theory. Adv. Math. 43 (1982), 250–283. Zbl0484.12004MR648801
  25. J.-P. Serre, Groupes de Galois sur . Sém. Bourbaki 1987-1988, no 689. Zbl0684.12009MR992203
  26. J.-P. Serre, Topics in Galois theory. Jones and Bartlett, Boston, 1992. Zbl0746.12001MR1162313
  27. R. Swan, Noether’s problem in Galois theory. J. D. Sally and B. Srinivasan, editors, Emmy Noether in Bryn Mawr. Springer (1983), 21–40. Zbl0538.12012MR713790
  28. N. Vila, On central extensions of A n as Galois group over . Arch. Math. 44 (1985), 424–437. Zbl0562.12011MR792366

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