Good reduction of elliptic modules
Good reduction of elliptic modules
复制标题
椭圆模的良好减少
DOI：
10.2969/jmsj/03430475
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发表时间：
1982
影响因子：
0.7
通讯作者：
Toyofumi Takahashi
中科院分区：
文献类型：
--
作者：
Toyofumi Takahashi
In this paper we give a criterion for good reduction of elliptic modules (Theorem 1, Section 2) which is an analogue of the criterion of N\’eron-Ogg\v{S}afarevi\v{c} for abelian varieties, cf. [7]. In the rest of the paper we give applications to elliptic modules of rank one over global function fields: In Section 3, the main theorem of complex multiplication of elliptic modules ([3] and [5]) is reformulated in a more relevant form to our subject (Theorem 2). Then, to each elliptic module we can associate the “Hecke character” (Theorem 3) so that the elliptic module has good reduction at a place $v$ if and only if the Hecke character is unramified at $v$ . In Section 4, we give a classification theoran (Theorem 4) by means of the Hecke characters. Ag an application, it will be shown that each rank-one elliptic module over a global function field $K$ has a K-form which has good reduction everywhere (Theorem 5).
