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arXiv · 2006.04789

Fitting invariants in equivariant Iwasawa theory

Takenori Kataoka
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Abstract

The main conjectures in Iwasawa theory predict the relationship between the Iwasawa modules and the $p$-adic $L$-functions. Using a certain proved formulation of the main conjecture, Greither and Kurihara described explicitly the (initial) Fitting ideals of the Iwasawa modules for the cyclotomic $\mathbb{Z}_p$-extensions of finite abelian extensions of totally real fields. In this paper, we generalize the algebraic theory behind their work by developing the theory of ``shifts of Fitting invariants.'' As applications to Iwasawa theory, we obtain a noncommutative version and a two-variable version of the work of Greither and Kurihara.

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Takenori Kataoka. 2020-06-08. Fitting invariants in equivariant Iwasawa theory. https://arxiv.org/abs/2006.04789

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