Galois module structure of elliptic curves over number fields / Caiqun Xiao.

Format:

Book

Manuscript

Microformat

Thesis/Dissertation

Author/Creator:

Xiao, Caiqun.

Contributor:

University of Pennsylvania.

Language:

English

Subjects (All):

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

Local Subjects:

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

Physical Description:

v, 38 pages ; 29 cm

Production:

1997.

Summary:

Suppose N/L is a finite Galois extension of number fields, and L contains an imaginary quadratic field K. Let E be an elliptic curve over L for which $End(E)=O\sb{K}$. We study the relation between the global Galois module structure of the ring of integers $O\sb{N}$ and semi-local Galois structure of E. We define an invariant $\sb{\chi}(E,\ N/L)$ in the class group of the group ring $O\sb{K}\lbrack G\rbrack$ which measures the difference between these two structures. If N/L is at most tamely ramified, we determine the class of $\sb{\chi}(E,\ N/L)$ in $Cl(O\sb{K}\lbrack G\rbrack$) in terms of $O\sb{N}$, provided that no place v of N such that either $N\sb{v}/L\sb{w}$ is ramified or E has bad reduction at w is anomalous for E.

Notes:

Thesis (Ph.D. in Mathematics) -- University of Pennsylvania, 1997.

Includes bibliographical references.

Local Notes:

University Microfilms order no.: 97-27319.

OCLC:

187470597