Semi-topological Galois Theory
- Resource Type
- Authors
- Hsuan-Yi Liao; Jyh-Haur Teh
- Source
- Algebra Colloquium. 22:687-706
- Subject
- Discrete mathematics
Algebra and Number Theory
Galois cohomology
Inverse Galois problem
Mathematics::Number Theory
Applied Mathematics
Fundamental theorem of Galois theory
Galois group
Splitting of prime ideals in Galois extensions
Topology
Differential Galois theory
Embedding problem
symbols.namesake
symbols
Galois extension
Mathematics
- Language
- ISSN
- 0219-1733
1005-3867
We introduce splitting coverings to enhance the well known analogy between field extensions and covering spaces. Semi-topological Galois groups are defined for Weierstrass polynomials and a Galois correspondence is proved. Combining results from braid groups, we solve the topological inverse Galois problem. As an application, symmetric and cyclic groups are realized over ℚ.