Cyclotomic units and stickelberger ideals over global function fields대역함수체 상에서의 원분단위원과 스티켈버거이데알

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In this thesis we study on the cyclotomic untis and the Stickelberger ideal of abelian extensions F/k, which are subfields of cyclotomic function fields over a global function field k. In chapter 1, we give a brief history about cyclotomic units and Stickelber ideals in number theory. In chapter 2, we give the theory of cyclotomic function fields briefly. We also give definitions and properties of the logarithm map, the restriction and corestriction map, the lattice index, which will be used throughout the paper. In chapter 3, we define the group of cyclotomic units $C_F$ and we calculate the index of $C_F$ in $O_F^*$, which involves the ideal class number of its maximal real subfield. In chapter 4, we define the Stickelberger ideals $I_{F}^{±}$ and $I_{F}$ and we calculate their indices $[R^{±} : I_{F}^{±}]$ and $[R : I_{F}]$, whose formulas involve the class numbers $h^{-}(O_{F})$, $h(F^+)$ and h(F), respectively. In chapter 5, we discuss on the indices $(R : U), (e^{+}R : e^{+}U)$ and $(e^{-}R : e^{-}U)$ which appear in our index-class number formulas and calculate them for some cases.
Advisors
Bae, Sung-Hanresearcher배성한researcher
Description
한국과학기술원 : 수학전공,
Publisher
한국과학기술원
Issue Date
2003
Identifier
180993/325007 / 000975201
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수학전공, 2003.2, [ iii, 38 p. ]

Keywords

global function fields; 스티켈버거이데알; cyclotomic units; Stickelberger ideal; 대역함수체; 원분단위원

URI
http://hdl.handle.net/10203/41860
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=180993&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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