Greenberg's Conjecture and Relative Unit Groups for Real Quadratic Fields
✍ Scribed by Takashi Fukuda
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 369 KB
- Volume
- 65
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
✦ Synopsis
to my teacher, professor tsuneo kanno, on his 70th birthday For an odd prime number p and a real quadratic field k, we consider relative unit groups for intermediate fields of the cyclotomic Z p -extension of k and discuss the relation to Greenberg's conjecture.
1997 Academic Press 2 which were defined generally in . In order to calculate n (2) 0 and n (2) 2 , we introduced the notion of relative unit group in . In this paper, we study the structure of the relative unit groups for all intermediate fields of the cyclotomic Z p -extension of k, and see that the relative unit group is closely related to Greenberg's conjecture.