Orders, field embeddings and the Eichler class number formula
Date Issued
2014
Date
2014
Author(s)
Yang, Tse-Chung
Abstract
This thesis is separated into three parts. In the first part, we consider a finite-dimensional central simple
algebra A over a global field F and a finite (separable or not) field extension K of F whose degree divides the degree
of A over K. We give the necessary and sufficient condition for which the field K (resp. K_v) can be F-linearly (resp.
F_v-linearly) embedded into A (resp. A_v). Here v is a place
of F, and F_v denotes the completion of F at v, K_v:=Kotimes_F F_v and A_v:=A otimes_F F_v. This yields a more numerical criterion for a pair (K,A) for which Hasse principle holds or not.
Secondly, we study a class of orders called monomial orders in a central simple algebra over a non-Archimedean local field and determine which monomial orders are
Gorenstein or Bass orders. In fact, we can show that for upper triangular monomial orders, the sets of Gorenstein orders and Eichler orders are the same. For general case, a monomial order is Bass if and only if it is either a hereditary or an Eichler order of period two.
The goal of the third part is to compute the number of mathbb{F}_p-isomorphism classes of abelian varieties in the simple isogeny class corresponding to the p-Weil number pi =sqrt{p}, where p is a prime integer. Main tools are the Honda-Tate theory and extended methods for Eichler''s class number formula.
Subjects
阿貝耳簇
巴斯秩序
中央簡單代數
埃奇勒類數公式
埃奇勒秩序
古瑞斯丹秩序
哈瑟原則
西利地特瑞秩序
本田-塔特理論
單項秩序
韋伊數
Type
thesis
File(s)![Thumbnail Image]()
Loading...
Name
ntu-103-D97221007-1.pdf
Size
23.54 KB
Format
Adobe PDF
Checksum
(MD5):5737e46f61515f7dcf846bf891c873f2