Research on the reciprocity law of local fields
Project/Area Number  09640045 
Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Algebra

Research Institution  Kagawa University 
Principal Investigator 
NAITO Hirotada Kagawa University of Education, A.P., 教育学部, 助教授 (00180224)

CoInvestigator(Kenkyūbuntansha) 
NAKAJIMA Shoichi Gakushuin, Science, P., 理学部, 教授 (90172311)

Project Period (FY) 
1997 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥2,500,000 (Direct Cost : ¥2,500,000)
Fiscal Year 1999 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1998 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1997 : ¥1,000,000 (Direct Cost : ¥1,000,000)

Keywords  Number Theo / local field 
Research Abstract 
We determine all extensions over the rational padic fields which are generated by 3 division points of elliptic curves, We see that there are three fields which are not generated by such points. As an application, we construct algebraic number fields whose Galois group over the rational number field are isomorphic to the general linear group of degree two over the prime field of three elements with some local conditions ( decomposition law). We construct infinitely many imaginary quadratic extensions over the fixed totally real number fields such that their relative class numbers are indivisible by the fixed odd prime with some loca conditions. We rediscover algebraic number fields such 'that their Dedekind zeta functions coincide but they are not conjugate, in the Galois extentions over the rational number fields whose Galois group over the rational number field are isomorphic to the general linear group of degree two over the prime field of p elements. Moreover we prove that the non p parts of the ideal class groups are isomorphic each other.

Report
(4results)
Research Products
(2results)