Semi-topological Galois theory and the inverse Galois problem

2010/06/07 by Hsuan-Yi Liao, Liao, Hsuan-Yi, Jyh-Haur Teh +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Number Theory (math.NT) #math.AG #math.GR #math.GT #math.NT

paper · pdf · doi:10.48550/arxiv.1006.1166

23 pages

arxiv created 2010/06/07 · arxiv updated 2010/06/08

Abstract

We enhance the analogy between field extensions and covering spaces by introducing the concept of splitting covering which correspondences to the splitting field in Galois theory. We define semi-topological Galois groups for Weierstrass polynomials and prove the existence of a Galois correspondence. This new tool enables us to study the inverse Galois problem from a new viewpoint.

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