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標題: | 無全域良化約之阿貝爾簇 There are no abelian schemes over Z |
作者: | Chun-Wei Lee 李俊緯 |
指導教授: | 陳其誠(Ki-Shen tan) |
關鍵字: | 阿貝爾簇,良化約,Fontaine 上界,Neron 模型,分冪理想, Abelian varieties,Good reduction,Fontaine bound,Neron model,Divided power ideals, |
出版年 : | 2017 |
學位: | 碩士 |
摘要: | 阿貝爾簇是一個有阿貝爾群結構的簇。這些簇是在多個數學領域裡有特別重要性的幾何物件。我們對於有理數上的阿貝爾簇在不同質數下的化約感興趣。特別的,我們想知道是否一個阿貝爾簇的化約仍然是阿貝爾簇。我們知道一個阿貝爾簇只會在有限個質數上的化約不是阿貝爾簇。不過一個阿貝爾簇不會在所有質數上的化約都是阿貝爾簇。
這是Fontaine的定理。但Fontaine的證明對於初學者來說並不容易,所以我展開證明中的細節,讓潛在的讀者更能了解。 A variety is called an abelian variety if it has an abelian group structure. These varieties are special geometric objects of particular importance in multiple mathematics fields. We are concerned with the reductions of abelian varieties over the field of rational numbers modulo different primes. In particular, we are interested in whether the reduction of an abelian variety remains an abelian variety. It is well-known for years that the reduction is still an abelian variety, except for finitely many primes. However, it cannot be an abelian variety modulo every prime. This is a theorem of Fontaine. But Fontaine's proof is not easy for beginners. So I expound the details of the proof to make it easier for potential readers. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/7759 |
DOI: | 10.6342/NTU201701790 |
全文授權: | 同意授權(全球公開) |
顯示於系所單位: | 數學系 |
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ntu-106-1.pdf | 532.2 kB | Adobe PDF | 檢視/開啟 |
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