Let be an odd prime number and a finite abelian -group. We describe the unit group of (the completion of the localization at of ) as well as the kernel and cokernel of the integral logarithm , which appears in non-commutative Iwasawa theory.
Soient un nombre premier impair et un groupe fini abélien. Nous décrivons le groupe d’unités de (la complétion du localisé de en ) ainsi que le noyau et le conoyau du logarithme intégral , qui apparaît dans la théorie d’Iwasawa non-commutative.
@article{JTNB_2010__22_1_197_0, author = {Ritter, J\"urgen and Weiss, Alfred}, title = {The integral logarithm in {Iwasawa} theory~: an exercise}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {197--207}, publisher = {Universit\'e Bordeaux 1}, volume = {22}, number = {1}, year = {2010}, doi = {10.5802/jtnb.711}, zbl = {1214.11124}, mrnumber = {2675880}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jtnb.711/} }
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 SP - 197 EP - 207 VL - 22 IS - 1 PB - Université Bordeaux 1 UR - http://archive.numdam.org/articles/10.5802/jtnb.711/ DO - 10.5802/jtnb.711 LA - en ID - JTNB_2010__22_1_197_0 ER -
%0 Journal Article %A Ritter, Jürgen %A Weiss, Alfred %T The integral logarithm in Iwasawa theory : an exercise %J Journal de théorie des nombres de Bordeaux %D 2010 %P 197-207 %V 22 %N 1 %I Université Bordeaux 1 %U http://archive.numdam.org/articles/10.5802/jtnb.711/ %R 10.5802/jtnb.711 %G en %F JTNB_2010__22_1_197_0
Ritter, Jürgen; Weiss, Alfred. The integral logarithm in Iwasawa theory : an exercise. Journal de théorie des nombres de Bordeaux, Volume 22 (2010) no. 1, pp. 197-207. doi : 10.5802/jtnb.711. http://archive.numdam.org/articles/10.5802/jtnb.711/
[1] C.W. Curtis and I. Reiner, Methods of Representation Theory, I,II. John Wiley & Sons, 1981, 1987. | Zbl
[2] B. Coleman, Local units modulo circular units. Proc. AMS 89 (1983), 1–7. | MR | Zbl
[3] I. Fesenko and M. Kurihara, Invitation to higher local fields. Geometry & Topology Monographs 3 (2000), ISSN 1464-8997 (online). | MR | Zbl
[4] A. Fröhlich, Galois Module Structure of Algebraic Integers. Springer-Verlag, 1983. | MR | Zbl
[5] T. Fukaya and K. Kato, A formulation of conjectures on -adic zeta functions in non-commutative Iwasawa theory. Proc. St. Petersburg Math. Soc. 11 (2005). | MR
[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). | MR | Zbl
[8] R. Oliver, Whitehead Groups of Finite Groups. LMS Lecture Notes Series 132, Cambridge (1988). | MR | Zbl
[9] J. Ritter and A. Weiss, Toward equivariant Iwasawa theory, II. Indagationes Mathematicae 15 (2004), 549–572. | MR | Zbl
[10] J. Ritter and A. Weiss, Toward equivariant Iwasawa theory, III. Mathematische Annalen 336 (2006), 27–49. | MR | Zbl
[11] J. Ritter and A. Weiss, Non-abelian pseudomeasures and congruences between abelian Iwasawa -functions. Pure and Applied Mathematics Quarterly 4 (2008), 1085–1106. | MR
[12] J. Ritter and A. Weiss, Congruences between abelian pseudomeasures. Math. Res. Lett. 15 (2008), 715–725. | MR | Zbl
[13] J. Ritter and A. Weiss, Equivariant Iwasawa theory : an example. Documenta Mathematica 13 (2008), 117–129. | MR
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