Forum Mathematicum ( IF 0.733 ) Pub Date : 2020-09-01 , DOI: 10.1515/forum-2019-0119
Sören Kleine

We study the generalised Iwasawa invariants of $ℤpd$-extensions of a fixed number field K. Based on an inequality between ranks of finitely generated torsion $ℤp⁢[[T1,…,Td]]$-modules and their corresponding elementary modules, we prove that these invariants are locally maximal with respect to a suitable topology on the set of $ℤpd$-extensions of K, i.e., that the generalised Iwasawa invariants of a $ℤpd$-extension $𝕂$ of K bound the invariants of all $ℤpd$-extensions of K in an open neighbourhood of $𝕂$. Moreover, we prove an asymptotic growth formula for the class numbers of the intermediate fields in certain $ℤp2$-extensions, which improves former results of Cuoco and Monsky. We also briefly discuss the impact of generalised Iwasawa invariants on the global boundedness of Iwasawa λ-invariants.

down
wechat
bug