A unified approach to the Galois closure problem

Hau Wen Huang, Wen Ching Winnie Li

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)251-279
Number of pages29
JournalJournal of Number Theory
Volume180
DOIs
StatePublished - Nov 2017

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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