The integral logarithm in Iwasawa theory : an exercise

Jürgen Ritter[1]; Alfred Weiss[2]

  • [1] Schnurbeinstraße 14 86391 Deuringen, Germany
  • [2] Department of Mathematics University of Alberta Edmonton, AB, Canada T6C 2G1

Journal de Théorie des Nombres de Bordeaux (2010)

  • Volume: 22, Issue: 1, page 197-207
  • ISSN: 1246-7405

Abstract

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Let l be an odd prime number and H a finite abelian l -group. We describe the unit group of Λ ∧ [ H ] (the completion of the localization at l of ℤ l [ [ T ] ] [ H ] ) as well as the kernel and cokernel of the integral logarithm L : Λ ∧ [ H ] × → Λ ∧ [ H ] , which appears in non-commutative Iwasawa theory.

How to cite

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Ritter, Jürgen, and Weiss, Alfred. "The integral logarithm in Iwasawa theory : an exercise." Journal de Théorie des Nombres de Bordeaux 22.1 (2010): 197-207. <http://eudml.org/doc/116395>.

@article{Ritter2010,
abstract = {Let $l$ be an odd prime number and $H$ a finite abelian $l$-group. We describe the unit group of $\Lambda _\wedge [H]$ (the completion of the localization at $l$ of $\mathbb\{Z\}_l[[T]][H]$) as well as the kernel and cokernel of the integral logarithm $L:\Lambda _\wedge [H]^\times \rightarrow \Lambda _\wedge [H]$, which appears in non-commutative Iwasawa theory.},
affiliation = {Schnurbeinstraße 14 86391 Deuringen, Germany; Department of Mathematics University of Alberta Edmonton, AB, Canada T6C 2G1},
author = {Ritter, Jürgen, Weiss, Alfred},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {integral logarithm; Iwasawa theory},
language = {eng},
number = {1},
pages = {197-207},
publisher = {Université Bordeaux 1},
title = {The integral logarithm in Iwasawa theory : an exercise},
url = {http://eudml.org/doc/116395},
volume = {22},
year = {2010},
}

TY - JOUR
AU - Ritter, Jürgen
AU - Weiss, Alfred
TI - The integral logarithm in Iwasawa theory : an exercise
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2010
PB - Université Bordeaux 1
VL - 22
IS - 1
SP - 197
EP - 207
AB - Let $l$ be an odd prime number and $H$ a finite abelian $l$-group. We describe the unit group of $\Lambda _\wedge [H]$ (the completion of the localization at $l$ of $\mathbb{Z}_l[[T]][H]$) as well as the kernel and cokernel of the integral logarithm $L:\Lambda _\wedge [H]^\times \rightarrow \Lambda _\wedge [H]$, which appears in non-commutative Iwasawa theory.
LA - eng
KW - integral logarithm; Iwasawa theory
UR - http://eudml.org/doc/116395
ER -

References

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  1. C.W. Curtis and I. Reiner, Methods of Representation Theory, I,II. John Wiley & Sons, 1981, 1987. Zbl0616.20001
  2. B. Coleman, Local units modulo circular units. Proc. AMS 89 (1983), 1–7. Zbl0528.12005MR706497
  3. I. Fesenko and M. Kurihara, Invitation to higher local fields. Geometry & Topology Monographs 3 (2000), ISSN 1464-8997 (online). Zbl0954.00026MR1804915
  4. A. Fröhlich, Galois Module Structure of Algebraic Integers. Springer-Verlag, 1983. Zbl0501.12012MR717033
  5. T. Fukaya and K. Kato, A formulation of conjectures on p -adic zeta functions in non-commutative Iwasawa theory. Proc. St. Petersburg Math. Soc. 11 (2005). Zbl1238.11105MR2276851
  6. K. Kato, Iwasawa theory of totally real fields for Galois extensions of Heisenberg type. Preprint (‘Very preliminary version’ , 2006) 
  7. S. Lang, Cylotomic Fields I-II. Springer GTM 121 (1990). Zbl0704.11038MR1029028
  8. R. Oliver, Whitehead Groups of Finite Groups. LMS Lecture Notes Series 132, Cambridge (1988). Zbl0636.18001MR933091
  9. J. Ritter and A. Weiss, Toward equivariant Iwasawa theory, II. Indagationes Mathematicae 15 (2004), 549–572. Zbl1142.11369MR2114937
  10. J. Ritter and A. Weiss, Toward equivariant Iwasawa theory, III. Mathematische Annalen 336 (2006), 27–49. Zbl1154.11038MR2242618
  11. J. Ritter and A. Weiss, Non-abelian pseudomeasures and congruences between abelian Iwasawa L -functions. Pure and Applied Mathematics Quarterly 4 (2008), 1085–1106. Zbl1193.11104MR2441694
  12. J. Ritter and A. Weiss, Congruences between abelian pseudomeasures. Math. Res. Lett. 15 (2008), 715–725. Zbl1158.11047MR2424908
  13. J. Ritter and A. Weiss, Equivariant Iwasawa theory : an example. Documenta Mathematica 13 (2008), 117–129. Zbl1243.11105MR2420909

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