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Journal of the Ramanujan Mathematical Society

Volume 38, Issue 1, March 2023  pp. 71–95.

Higher codimension behavior in equivariant Iwasawa theory for CM-fields

Authors:  Takenori Kataoka
Author institution: Department of Mathematics, Faculty of Science Division II, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

Summary:  In classical Iwasawa theory, we mainly study codimension one behavior of arithmetic modules. Relatively recently, F. M. Bleher, T. Chinburg, R. Greenberg, M. Kakde, G. Pappas, R. Sharifi, and M. J. Taylor started studying higher codimension behavior of unramified Iwasawa modules which are conjectured to be pseudo-null. In this paper, by developing a general algebraic theory on perfect complexes, we obtain a new perspective of their work. That allows us to extend the results to equivariant settings and, even in non-equivariant settings, to obtain more refined results concerning the higher codimension behavior.

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