3 citations · 11 across the 16 of their papers we have counts for
15 papers · 1 filter
On derivatives of Kato's Euler system and the Mazur-Tate Conjecture
David Burns, Masato Kurihara, Takamichi Sano
We provide a new interpretation of the Mazur-Tate Conjecture and then use it to obtain the first (unconditional) theoretical evidence in support of the conjecture for elliptic curv…
Notes on the dual of the ideal class groups of CM-fields
Masato Kurihara
In this paper, for a CM abelian extension of number fields, we propose a conjecture which describes completely the Fitting ideal of the minus part of the Pontryagin dual of t…
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…
On derivatives of Kato's Euler system for elliptic curves
David Burns, Masato Kurihara, Takamichi Sano
In this paper we study a new conjecture concerning Kato's Euler system of zeta elements for elliptic curves over . This conjecture, which we refer to as the `Genera…
On the refined conjectures on Fitting ideals of Selmer groups of elliptic curves with supersingular reduction
Chan-Ho Kim, Masato Kurihara
In this paper, we study the Fitting ideals of Selmer groups over finite subextensions in the cyclotomic -extension of of an elliptic curve over $\mathbb{…
On Stark elements of arbitrary weight and their -adic families
David Burns, Masato Kurihara, Takamichi Sano
We develop a detailed arithmetic theory related to special values at arbitrary integers of the Artin -series of linear characters. To do so we define canonical generalized Stark…
Iwasawa theory and zeta elements for
David Burns, Masato Kurihara, Takamichi Sano
We describe an explicit `higher rank' Iwasawa theory for zeta elements associated to the multiplicative group over abelian extensions of general number fields. We then show that th…
The structure of Selmer groups of elliptic curves and modular symbols
Masato Kurihara
For an elliptic curve over the rational number field and a prime number , we study the structure of the classical Selmer group of -power torsion points. In our previous paper…
On zeta elements for
David Burns, Masato Kurihara, Takamichi Sano
In this paper, we present a unifying approach to the general theory of abelian Stark conjectures. To do so we define natural notions of `zeta element', of `Weil-étale cohomology co…
Invitation to higher local fields, Part I, section 13: Abelian extensions of absolutely unramified complete discrete valuation fields
Masato Kurihara
This is an introduction to the author theory of cyclic p-extensions of an absolutely unramified complete discrete valuation field K with arbitrary residue field of characteristic p…
Invitation to higher local fields, Part I, section 12: Two types of complete discrete valuation fields
Masato Kurihara
This work sketches the author classification of complete discrete valuation fields K of characteristic 0 with residue field of characteristic p into two classes depending on the be…
Invitation to higher local fields, Part I, section 9: Exponential maps and explicit formulas
Masato Kurihara
An exponential homomorphism for a complete discrete valuation field of characteristic zero which relates differential forms and the Milnor K-groups of the field is studied. An appl…
Invitation to higher local fields, Part I, section 5: Kato's higher local class field theory
Masato Kurihara
This is a presentation of main ingredients of Kato's higher local class field theory.
Invitation to higher local fields, Part I, section A: Appendix to Section 2
Masato Kurihara, Ivan Fesenko
This appendix discusses some basic definitions and properties of differential forms and Kato's cohomology groups in characteristic p and a sketch of the proof of Bloch-Kato-Gabber'…
Invitation to higher local fields (Introduction)
Ivan Fesenko, Masato Kurihara
The monograph "Invitation to higher local fields" is the result of the conference on higher local fields held in Muenster, August 29 to September 5, 1999. The aim is to provide an…