Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T01:41:29.607Z Has data issue: false hasContentIssue false

A Relation Between the 2-Primary Parts of the Main Conjecture and the Birch-Tate-Conjecture

Published online by Cambridge University Press:  20 November 2018

Manfred Kolster*
Affiliation:
Westf. Wilhelms-Universität, Math. Institut, Einsteinstr. 62 D-4400 Münster, West-Germany
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that for totally real number fields the Main Conjecture in Iwasawa-Theory for p = 2 proposed by Fédérer implies the 2-primary part of the Birch-Tate-Conjecture in analogy with the case p odd.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Coates, J., On K2 and some classical conjectures in algebraic number theory, Ann. of Math. 95 (1972), 99-116.Google Scholar
2. p-adic L-functions and Iwasawa's theory, in A. Frôhlich (éd.): Algebraic Number Fields, Academic Press, London (1977), 227286.Google Scholar
3. Deligne, P. and Ribet, K., Values of abelian L-functions at negative integers over totally real fields, Inv. math. 59 (1980), 227-286.Google Scholar
4. F, L. J.édérer, Regulators, Iwasawa Modules, and the Main Conjecture for p = 2, in N. Koblitz (éd.): Number Theory related to Fermat's Last Theorem, Birkhàuser, Basel (1982), 289-296.Google Scholar
5. Iwasawa, K., On cohomology groups of units for Tup-extensions, Am. J. of Math. 105 (1983), 189-200.Google Scholar
6. Kolster, M., The structure of the 2-Sylow-subgroup of #2(0), I, Comm. Math. Helv. 61 (1986), 376-388.Google Scholar
7. The structure of the 2-Sy low-sub group of K2(o), II, K-theory, 1 (1987), 467-479.Google Scholar
8. Lichtenbaum, S., On the values of zeta and L-functions, I, Ann. of Math. 96 (1972), 388-360.Google Scholar
9. Mazur, B. and Wiles, A., Class fields of abelian extensions ofQ, Inv. Math. 76 (1984), 179-330.Google Scholar