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| 研究生： |
鍾明廷 Zhong, Ming-Ting |
|---|---|
| 論文名稱： |
The Galois Group of Iterated Polynomial of X^{p^r}-c over Non-archimedean Valued Field The Galois Group of Iterated Polynomial of X^{p^r}-c over Non-archimedean Valued Field |
| 指導教授： |
夏良忠
Hsia, Liang-Chung |
| 學位類別： |
碩士 Master |
| 系所名稱： |
數學系 Department of Mathematics |
| 論文出版年： | 2020 |
| 畢業學年度： | 108 |
| 語文別： | 英文 |
| 論文頁數： | 34 |
| 英文關鍵詞： | infinitely wildly ramified |
| DOI URL： | http://doi.org/10.6345/NTNU202000914 |
| 論文種類： | 學術論文 |
| 相關次數： | 點閱：147 下載：23 |
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Let K be a finite extension over Q_p the fraction field of p-adic integers. Let f(X) =X^{p^r} - c ∈ K[X] where r ∈ Z≥2, and let f_n(X) be the nth iterated polynomial of
f(X). For any a ∈ K, we examine the Galois groups and the ramified index of K_n over K where K_n is the splitting field of f_n(X) − a over K. For some v(c), the behavior
depends on v(c). But for
-p/(p-1) - (r-1)p^r/(p^r-1) ≤ v(c) < -p/(p-1),
we haven’t found results.
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