Comparing direct limit and inverse limit of even K-groups in multiple ℤ p -extensions
Meng Fai Lim1
1 School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences Central China Normal University Wuhan, 430079, P. R. China
Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 2, pp. 537-555.

Iwasawa a établi une dualité entre la limite directe et la limite inverse des groupes des classes dans une ℤ p -extension. Récemment, ce résultat a été généralisé au cas de ℤ p -extensions multiples par de nombreux auteurs. Dans cet article, nous établissons une dualité analogue entre la limite directe et la limite inverse des K-groupes en degrés pairs dans une ℤ p d -extension. Nous donnons ensuite quelques exemples où la limite directe peut être nulle ou pas.

Iwasawa first established a duality relating the direct limit and the inverse limit of class groups in a ℤ p -extension, and this result has recently been extended to multiple ℤ p -extensions by many authors. In this paper, we establish an analogous duality for the direct limit and the inverse limit of higher even K-groups in a ℤ p d -extension. We then give some examples where the direct limit may or may not vanish.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/jtnb.1288
Classification : 11R23, 11R70, 11S25
Mots clés : Even $K$-groups, $\mathbb{Z}_p^d$-extension.
Meng Fai Lim 1

1 School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences Central China Normal University Wuhan, 430079, P. R. China
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Meng Fai Lim. Comparing direct limit and inverse limit of even $K$-groups in multiple $\mathbb{Z}_p$-extensions. Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 2, pp. 537-555. doi : 10.5802/jtnb.1288. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1288/

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