A unified approach to the Galois closure problem
In this paper we give a unified approach in categorical setting to the problem of finding the Galois closure of a finite cover, which includes as special cases the familiar finite separable field extensions, finite unramified covers of a connected undirected graph, finite covering spaces of a locall...
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| Published in: | Journal of number theory Vol. 180; pp. 251 - 279 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Elsevier Inc
01.11.2017
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| ISSN: | 0022-314X, 1096-1658 |
| Online Access: | Get full text |
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| Abstract | In this paper we give a unified approach in categorical setting to the problem of finding the Galois closure of a finite cover, which includes as special cases the familiar finite separable field extensions, finite unramified covers of a connected undirected graph, finite covering spaces of a locally connected topological space, finite étale covers of a smooth projective irreducible algebraic variety, and finite covers of normal varieties. We present two algorithms whose outputs are shown to be desired Galois closures. An upper bound of the degree of the Galois closure under each algorithm is also obtained. |
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| AbstractList | In this paper we give a unified approach in categorical setting to the problem of finding the Galois closure of a finite cover, which includes as special cases the familiar finite separable field extensions, finite unramified covers of a connected undirected graph, finite covering spaces of a locally connected topological space, finite étale covers of a smooth projective irreducible algebraic variety, and finite covers of normal varieties. We present two algorithms whose outputs are shown to be desired Galois closures. An upper bound of the degree of the Galois closure under each algorithm is also obtained. |
| Author | Li, Wen-Ching Winnie Huang, Hau-Wen |
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| Keywords | 68W05 Iterative algorithms Divide-and-conquer algorithms 11R32 Galois closures |
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| References | Bailey, Fried (br0010) 2002; vol. 70 Cohen (br0030) 1996; vol. 138 Fried, Völklein (br0060) 1991; 290 Mac Lane (br0090) 1998; vol. 5 Fried, Ihara (br0040) 2002; vol. 70 Cormen, Leiserson, Rivest, Stein (br0020) 2009 Fröhlich, Shepherson (br0050) 1955; 62 Fried, Völklein (br0070) 1992; 135 von zur Gathen, Gerhard (br0110) 2013 Terras (br0100) 2010; vol. 128 Hell (br0080) 1972 Fröhlich (10.1016/j.jnt.2017.04.011_br0050) 1955; 62 Bailey (10.1016/j.jnt.2017.04.011_br0010) 2002; vol. 70 von zur Gathen (10.1016/j.jnt.2017.04.011_br0110) 2013 Fried (10.1016/j.jnt.2017.04.011_br0040) 2002; vol. 70 Hell (10.1016/j.jnt.2017.04.011_br0080) 1972 Cormen (10.1016/j.jnt.2017.04.011_br0020) 2009 Fried (10.1016/j.jnt.2017.04.011_br0060) 1991; 290 Cohen (10.1016/j.jnt.2017.04.011_br0030) 1996; vol. 138 Fried (10.1016/j.jnt.2017.04.011_br0070) 1992; 135 Mac Lane (10.1016/j.jnt.2017.04.011_br0090) 1998; vol. 5 Terras (10.1016/j.jnt.2017.04.011_br0100) 2010; vol. 128 |
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| Title | A unified approach to the Galois closure problem |
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