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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