We first compare the settings between Ritter-Weiss's equivariant Iwasawa theory and non-commutative Iwasawa theory à la Coates et al. in some details. We then discuss the strategy of Ritter and Weiss towards the proof of the “main conjecture” of their equivariant Iwasawa theory.
In appendices, we also deal with Chinburg's conjecture and the lifted root number conjecture à la Gruenberg, Ritter and Weiss, which are deeply related to the works of Ritter and Weiss on equivariant Iwasawa theory. This article is written in Japanese.
This is a survey article on so-called Burns-Kato's technique, which forms the basis of the proof of the non-commutative Iwasawa main conjecture. Written in Japanese.
Takashi Hara:
Concerning actions of 3-manifold groups: from topological and arithmetic viewpoints
RIMS Kôkyûroku “Intelligence of Low-dimensional Topology”, 1911, 57 – 75 (2014) Link
Survey of my joint work with Takahiro Kitayama on the construction of essential tribranched surfaces utilising geometry on character varieties of higher dimension. It also contains review of the classical Culler-Shalen theory. Written in English.
Takashi Hara: On the Iwasawa main conjecture for Hilbert modular forms with complex multiplication
Proceedings of the 58th Algebra Symposium, 213 – 245 (2013) Link
Survey article on the joint work with Tadashi Ochiai in which we discuss the cyclotomic Iwasawa main conjecture for Hilbert cuspforms with complex multiplication. We also deal with the elliptic case as a classical example. Written in Japanese.
Takashi Hara: On Culler-Shalen theory for 3-manifolds and related topics
Proceedings of the 17th Waseda Number Theory Symposium, 60 – 80 (2013) pdf file.
After a brief survey of classical Culler-Shalen theory for 3-manifolds, we discuss its extension to character varieties for higher rank representations and its application towards arithmetic topology. Written in Japanese.
Takashi Hara: On non-commutative
Iwasawa main conjectures for totally real number fields
RIMS Kôkyûroku Bessatsu, B32, 83 – 104 (2012) Link
Survey article on recent development of
study on the non-commutative Iwasawa main conjecture for
totally real number fields, written in Japanese.
Survey article on special values of L-functions. I wrote Part I
(theory on pure motives of Grothendieck) and Part IV
(Beilinson conjecture and Tamagawa number conjecture). This article is
written in Japanese.
Arguments on congruences between p-adic zeta functions deduced from non-commutative Iwasawa main conjecture, written in Japanese.
Takashi Hara: On non-commutative Iwasawa theory of
totally real number fields
RIMS Kôkyûroku Bessatsu, B19, 277 – 299 (2010) Link.
Survey article on non-commutative Iwasawa theory and strategy for
construction of non-commutative p-adic zeta functions for totally real number
fields, written in Japanese.
Survey article written in Japanese on the thesis
A family of Calabi-Yau varieties and potential modularity
of Michael Harris, Nick Shepherd-Barron and Richard Taylor,
especially concentrated on application of so-called "(l,l')-trick" to
Sato-Tate conjecture.