Semi-topological Galois theory and the inverse Galois problem
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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2010
- DOI:
- 10.48550/arXiv.1006.1166
- arXiv:
- arXiv:1006.1166
- Bibcode:
- 2010arXiv1006.1166L
- Keywords:
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- Mathematics - Group Theory;
- Mathematics - Algebraic Geometry;
- Mathematics - Geometric Topology;
- Mathematics - Number Theory
- E-Print:
- 23 pages