半拓撲伽羅瓦群論及反伽羅瓦問題

Semi-topological Galois theory and the inverse Galois problem

廖軒毅(Hsuan-Yi Liao)

指導教授 ： 鄭志豪

國立清華大學/理學院/數學系/碩士(2010年)

https://doi.org/10.6843/NTHU.2010.00086

摘要

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.

關鍵字

伽羅瓦群 ； 拓撲 ； 反伽羅瓦問題

並列摘要

無資料

並列關鍵字

topology ； Galois ； inverse Galois problem

參考文獻

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[7] D. Husemoller, Fibre Bundles, Graduate Texts in Mathematics 20, Springer-Verlag (1966).