The Galois Group of Iterated Polynomial of X^{p^r}-c over Non-archimedean Valued Field
| dc.contributor | 夏良忠 | zh_TW |
| dc.contributor | Hsia, Liang-Chung | en_US |
| dc.contributor.author | 鍾明廷 | zh_TW |
| dc.contributor.author | Zhong, Ming-Ting | en_US |
| dc.date.accessioned | 2020-12-14T09:00:16Z | |
| dc.date.available | 2020-07-29 | |
| dc.date.available | 2020-12-14T09:00:16Z | |
| dc.date.issued | 2020 | |
| dc.description.abstract | none | zh_TW |
| dc.description.abstract | 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. | en_US |
| dc.description.sponsorship | 數學系 | zh_TW |
| dc.identifier | G060740013S | |
| dc.identifier.uri | http://etds.lib.ntnu.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dstdcdr&s=id=%22G060740013S%22.& | |
| dc.identifier.uri | http://rportal.lib.ntnu.edu.tw:80/handle/20.500.12235/111254 | |
| dc.language | 英文 | |
| dc.subject | none | zh_TW |
| dc.subject | iterated polynomial | en_US |
| dc.subject | arboreal Galois group | en_US |
| dc.subject | infinitely wildly ramified | en_US |
| dc.title | The Galois Group of Iterated Polynomial of X^{p^r}-c over Non-archimedean Valued Field | zh_TW |
| dc.title | The Galois Group of Iterated Polynomial of X^{p^r}-c over Non-archimedean Valued Field | en_US |
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