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Generalised Iwasawa invariants and the growth of class numbers
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 pd-extensions of a fixed number field K. Based on an inequality between ranks of finitely generated torsion p[[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 pd-extensions of K, i.e., that the generalised Iwasawa invariants of a pd-extension 𝕂 of K bound the invariants of all pd-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 p2-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.
更新日期:2020-09-18

 

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