TY - JOUR
T1 - A unified approach to the Galois closure problem
AU - Huang, Hau Wen
AU - Li, Wen Ching Winnie
N1 - Funding Information:
This research started when both authors were working at the National Center for Theoretical Sciences in Hsinchu, Taiwan. The research of the first author is partially supported by the Ministry of Science and Technology of Taiwan under the project MOST 105-2115-M-008-013. Part of the research was done when he was supported by the National Center for Theoretical Sciences of Taiwan and the Council for Higher Education of Israel. ?The research of the second author is partially supported by the NSF grant DMS-1101368 and the Simons Foundation grant # 355798. Part of the research was done when the author was visiting the National Tsing Hua University in summer 2015 and the Institute of Mathematics, Academia Sinica in spring and summer 2016. She would like to thank NCTS, the Mathematics Department of NTHU, and the Institute of Mathematics, Academia Sinica for their hospitality.
Publisher Copyright:
© 2017 Elsevier Inc.
PY - 2017/11
Y1 - 2017/11
N2 - 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.
AB - 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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U2 - 10.1016/j.jnt.2017.04.011
DO - 10.1016/j.jnt.2017.04.011
M3 - Article
AN - SCOPUS:85020403625
VL - 180
SP - 251
EP - 279
JO - Journal of Number Theory
JF - Journal of Number Theory
SN - 0022-314X
ER -