Galois groups of fields of definition of solvable branched coverings

Sybilla Beckmann

Compositio Mathematica (1988)

  • Volume: 66, Issue: 2, page 121-144
  • ISSN: 0010-437X

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Beckmann, Sybilla. "Galois groups of fields of definition of solvable branched coverings." Compositio Mathematica 66.2 (1988): 121-144. <http://eudml.org/doc/89901>.

@article{Beckmann1988,
author = {Beckmann, Sybilla},
journal = {Compositio Mathematica},
keywords = {small field of definition; solvable branched covering},
language = {eng},
number = {2},
pages = {121-144},
publisher = {Kluwer Academic Publishers},
title = {Galois groups of fields of definition of solvable branched coverings},
url = {http://eudml.org/doc/89901},
volume = {66},
year = {1988},
}

TY - JOUR
AU - Beckmann, Sybilla
TI - Galois groups of fields of definition of solvable branched coverings
JO - Compositio Mathematica
PY - 1988
PB - Kluwer Academic Publishers
VL - 66
IS - 2
SP - 121
EP - 144
LA - eng
KW - small field of definition; solvable branched covering
UR - http://eudml.org/doc/89901
ER -

References

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  1. [B] S. Beckmann: Fields of definition of solvable branched coverings, University of Pennsylvania Ph.D. thesis (1986). 
  2. [Bel] G.V. Belyi: On Galois extensions of a maximal cyclotomic field, Math. USSR Izv.14 (1980) 247-256. Zbl0429.12004MR534593
  3. [Bel2] G.V. Belyi: On extensions of the maximal cyclotomic field having a given classical Galois group, J. reine u. angew. Math.341 (1983) 147-156. Zbl0515.12008MR697314
  4. [C + H] K. Coombes and D. Harbater: Hurwitz families and arithmetic Galois groups, Duke Math. J.52, no. 4 (1985) 821-839. Zbl0601.14023MR816387
  5. [Ft] W. Feit, Ã5 and Ã7 are Galois groups over number fields, preprint (1986). MR866773
  6. [Fr] M. Fried, Fields of definition of function fields and Hurwitz families - Groups as Galois groups, Comm. Alg.5 (1977) 17-82. Zbl0478.12006MR453746
  7. [F] W. Fulton, Hurwitz schemes and irreducibility of algebraic curves, Ann. Math., ser. 2, 90 (1969) 542-575. Zbl0194.21901MR260752
  8. [G] D. Gorenstein, Classifying the finite simple groups, Bulletin of AMS, 14, no. 1 (1986) 1-98. Zbl0585.20003MR818060
  9. [Hall] M. Hall, Jr., The Theory of Groups, Chelsea, NY (1976). Zbl0354.20001
  10. [Ha] D. Harbater, Galois coverings of the arithmetic line, to appear in Proc. of the NY Number Thy. Conf. of 1985, LNM?, Springer. Zbl0627.12015MR894511
  11. [H] R. Hartshorne, Algebraic Geometry, Springer, NY (1977). Zbl0367.14001MR463157
  12. [L AV] S. Lang, Abelian Varieties, Interscience, NY (1959). Zbl0098.13201MR106225
  13. [L DG] S. Lang, Fundamentals of Diophantine Geometry, Springer, NY (1985). Zbl0528.14013MR715605
  14. [M1] B. Matzat, Konstruktion von Zahl- und Funktionenkörpern mit vorgegebener Galoisgrouppe, J. reine u. angew. Math.349 (1984) 179-220. Zbl0555.12005MR743971
  15. [M2] B. Matzat, Zwei Aspekte konstruktiver Galoistheorie, J. Algebra96 (1985) 449-531. Zbl0587.12004MR810543
  16. [M3] B. Matzat, Über das Umkehrproblem der galoisschen Theorie, Karlsruhe (1985), preprint. MR988071
  17. [N] J. Neukirch, On Solvable Number Fields, Inventiones Math.53 (1979) 135-164. Zbl0447.12008MR560411
  18. [Sh] I.R. Šafarevič, Construction of fields of algebraic numbers with given solvable galois group, Izv. Akad. Nauk. SSSR. Ser. Math.18 (1954) 525-578; AMS Transl., Ser. 2, 4 (1956) 185-237. Zbl0071.03307MR71469
  19. [GAGA] J.-P. Serre, Géometrie algebrique et géometrie analytique, Ann. de L'Inst. FourierVI (1956) 1-42. Zbl0075.30401MR82175
  20. [Se l] J.-P. Serre, Abelian l-adic Representations and Elliptic Curves, W.A. Benjamin, NY (1968). Zbl0186.25701MR263823
  21. [Se LF] J.-P. Serre, Local Fields, Springer, NY (1979). Zbl0423.12016MR554237
  22. [Se PG] J.-P. Serre, Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Inv. Math.15 (1972) (259-331). Zbl0235.14012MR387283
  23. [Si] J.H. Silverman, The Arithmetic of Elliptic Curves, Springer, NY (1986). Zbl0585.14026MR817210
  24. [Th] J. Thompson, Some finite groups which appear as Gal (L/K) where K ⊂ Q(μn), J. Alg.89 (1984) 437-499. Zbl0552.12004

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