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研究生： 王薇淳
Wang, Wei-Chun
論文名稱： 希爾伯特布魯蒙索卡利茲模之研究
Topic on Hilbert-Blumenthal-Carlitz Module
指導教授： 魏福村
Wei, Fu-Tsun
口試委員: 于靖
Yu, Jing
張介玉
Chang, Chieh-Yu
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2022
畢業學年度： 110
語文別： 英文
論文頁數： 31
中文關鍵詞： t-模 、扭點 、伽羅瓦表現
外文關鍵詞： t-module, torsion, Galois representation
相關次數： 點閱：3  下載：0 
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    • 在本論文中，我們利用卡利茲模的直和來建構最簡單的高維度希爾伯特布魯蒙
    索t模。並且透過海斯所提出的明確類體論去探討其伽羅瓦表示。

    In the thesis, we construct the simplest example of Hilbert-Blumenthal t-modules in the higher dimensional case by considering the direct sum of Carlitz modules. Also, we study the Galois representation associated with the Hilbert-Blumenthal t-modules in our case via the explicit class field theory developed by Hayes.

    1 Introduction 1 2 Preliminaries 4 2.1 NotationsandDefinitions 4 2.2 Class Field Theory and Chebotarev Density Theorem 4 2.3 RealQuadraticExtension 7 2.3.1 NumberFields 7 2.3.2 FunctionFields 9 3 Anderson t-modules 10 3.1 Background on Anderson t-modules 10 3.2 Hilbert-Blumenthal O_K-module 13 3.3 Tate Modules and Galois Representations 14 3.4 Cyclotomic Function Fields 16 4 2-dimensional H-B-C module 19 4.1 Module Structure of the C^D-torsion 22 4.2 Galois Action on the C^D-torsion 25 4.3 Galois Representation of H-B-C Module 28 Reference 31

    David A.Cox, Primes of the form x2 + ny2: Fermat, class field theory, and com- plex multiplication, Wiley, 2013.

    Greg W Anderson, t-motives, Duke Mathematical Journal 53 (1986), no. 2, 457–502.

    W. Dale Brownawell, Chieh-Yu Chang, Matthew A. Papanikolas, and Fu- Tsun Wei, Function field analogue of shimura’s conjecture on period symbols.

    F. Diamond and J. Shurman, A first course in modular forms, Graduate Texts in Mathematics, Springer New York, 2006.

    David Goss, Basic structures of function field arithmetic, Springer, Berlin, Hei- delberg, 1998.

    D.R. Hayes, Explicit class field theory for rational function fields, Transactions of the American Mathematical Society 189 (1974), 77–91.

    Kenneth Ireland and Michael Rosen, A classical introduction to modern num- ber theory, vol. 84, Springer Science, 1990.

    Serge Lang, Algebraic number theory, vol. 110, Springer Science, 1986. Mihran Papikian, Drinfeld module.

    Michael Rosen, Number theory in function fields, vol. 210, Springer Science & Business Media, 2002.

    J.P. Serre, Abelian l-adic representations and elliptic curves, Research Notes in Mathematics (A K Peters), Vol 7, Peters, 1998.

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