5 citations · 9 across the 16 of their papers we have counts for
16 papers
On the local equivariant Tamagawa number conjecture for Tate motives
Mahiro Atsuta, Naoto Dainobu, Takenori Kataoka
The local equivariant Tamagawa number conjecture (local ETNC) for a motive predicts a precise relationship between the local arithmetic complex and the root numbers which appear in…
Determining class groups as Galois modules up to equivalence for some nonabelian extensions
Cornelius Greither, Takenori Kataoka
In previous papers, the Galois module structure of minus class groups was studied for abelian CM extensions. In this paper, we discuss some nonabelian cases, focusing on metacyclic…
Rarity of pseudo-null Iwasawa modules for -adic Lie extensions
Takenori Kataoka
In this paper, we obtain a necessary and sufficient condition for the pseudo-nullity of the -ramified Iwasawa module for -adic Lie extension of totally real fields. It is app…
On the Galois module structure of minus class groups
Cornelius Greither, Takenori Kataoka
The main object of this paper is the minus class groups associated to CM-fields as Galois modules. In a previous article of the authors, we introduced a notion of equivalence for m…
Minimal resolutions of Iwasawa modules
Takenori Kataoka, Masato Kurihara
In this paper, we study the module-theoretic structure of classical Iwasawa modules. More precisely, for a finite abelian -extension of totally real fields and the cycloto…
Fitting ideals of Jacobian groups of graphs
Takenori Kataoka
The Jacobian group of a graph is a finite abelian group through which we can study the graph in an algebraic way. When the graph is a finite abelian covering of another graph, the…
Higher codimension Iwasawa theory for elliptic curves with supersingular reduction
Takenori Kataoka
Bleher et al. began studying higher codimension Iwasawa theory for classical Iwasawa modules. Subsequently, Lei and Palvannan studied an analogue for elliptic curves with supersing…
On Euler systems for motives and Heegner points
Takenori Kataoka, Takamichi Sano
We formulate an Iwasawa main conjecture for a higher rank Euler system for a general motive. We prove "one half" of the main conjecture under mild hypotheses. We also formulate a c…
On the minus component of the equivariant Tamagawa number conjecture for
Mahiro Atsuta, Takenori Kataoka
The equivariant Tamagawa number conjecture (hereinafter called the eTNC) predicts close relationships between algebraic and analytic aspects of motives. In this paper, we prove a l…
Fitting ideals of class groups for CM abelian extensions
Mahiro Atsuta, Takenori Kataoka
Let be a finite abelian CM-extension and a suitable finite set of finite primes of . In this paper, we determine the Fitting ideal of the minus component of the -ra…
Higher codimension behavior in equivariant Iwasawa theory for CM-fields
Takenori Kataoka
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. S…
Fitting ideals in two-variable equivariant Iwasawa theory and an application
Takenori Kataoka
We study equivariant Iwasawa theory for two-variable abelian extensions of an imaginary quadratic field. One of the main goals of this paper is to describe the Fitting ideals of Iw…
Equivariant Iwasawa theory for elliptic curves
Takenori Kataoka
We discuss abelian equivariant Iwasawa theory for elliptic curves over at good supersingular primes and non-anomalous good ordinary primes. Using Kobayashi's method, w…
Fitting ideals of -ramified Iwasawa modules over totally real fields
Cornelius Greither, Takenori Kataoka, Masato Kurihara
We completely calculate the Fitting ideal of the classical -ramified Iwasawa module for any abelian extension of totally real fields, using the shifted Fitting ideals rece…
Fitting invariants in equivariant Iwasawa theory
Takenori Kataoka
The main conjectures in Iwasawa theory predict the relationship between the Iwasawa modules and the -adic -functions. Using a certain proved formulation of the main conjectur…
A consequence of Greenberg's generalized conjecture on Iwasawa invariants of -extensions
Takenori Kataoka
For a prime number and a number field , let be the compositum of all -extensions of . Greenberg's Generalized Conjecture (GGC) claims the pseudo…