Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-05-25T19:14:52.500Z Has data issue: false hasContentIssue false
  • English
  • Français

The Cohomology of the Units in Certain Zp-Extensions

Published online by Cambridge University Press:  20 November 2018

H. Kisilevsky
H. Kisilevsky*
Affiliation:
Department of Mathematics, Concordia UniversityMontreal, Quebec H3G 1M8, Canada
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.

For K/k a Zp-extension with Galois group Γ Iwasawa in [4], poses the question of determining the cohomology groups Hn (Γ, E) of the unit group E of K. In this article we compute the cohomology of the units (up to finite groups) for a certain class of Zp-extensions.

Keywords

12A6012A45
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 3 , 01 September 1985 , pp. 350 - 354
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Carrol, J. and Kisilevsky, H., On Iwasawa's λ-invariantfor certain Zl extensions, Acta Arithmetica XL (1981), pp. 1–8.Google Scholar
2. , On the Iwasawa invariants of certain Zp-extensions, Compositio Math. 49 (1983), pp. 217–229.Google Scholar
3. Greenberg, R., On a certain p-adic representation, Inventiones Math. 21 (1973), pp. 117—124 Google Scholar
4. Iwasawa, K., On cohomology groups of units for Zp-extensions, American Jour, of Math. Vol. 105, No. 1 (1983), pp. 189–200.Google Scholar
5. Jaulent, J.F., Sur la théorie des genres dans une extension procyclique métabelienne sur un sous corps, To appear.Google Scholar
6. Kisilevsky, H., Some non-semi-simple Iwasawa modules, Compositio Math. 49 (1983), pp. 399–404.Google Scholar
7. Kisilevsky, H., On the semi-simplicity of a certain Iwasawa module, Submitted to Can. J. of Math.Google Scholar