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On the field of definition for modularity of CM elliptic curves

✍ Scribed by Naoki Murabayashi

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
321 KB
Volume
108
Category
Article
ISSN
0022-314X

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✦ Synopsis

The purpose of this paper is to decide the conditions under which a CM elliptic curve is modular over its field of definition.

πŸ“œ SIMILAR VOLUMES

Modularity of CM elliptic curves over di
Modularity of CM elliptic curves over division fields
✍ Naoki Murabayashi πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 91 KB

Let E be a CM elliptic curve defined over an algebraic number field F . In general E will not be modular over F . In this paper, we determine extensions of F , contained in suitable division fields of E, over which E is modular. Under some weak assumptions on E, we construct a minimal subfield of di

On the Tamagawa Number Conjecture for CM
On the Tamagawa Number Conjecture for CM Elliptic Curves Defined Over Q
✍ Francesc Bars πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 206 KB

In this paper we prove, under the assumption that the SouleΒ΄regulator map is injective, that, for all integers k50, the description by the local Tamagawa number conjecture for CM elliptic curves defined over Q, corresponding to the values of their L-functions at k ΓΎ 2, is true.