Grant-in-Aid for Scientific Research (C)
|Allocation Type||Single-year Grants|
|Research Institution||Nagoya University|
FUJIWARA Kazuhiro Nagoya univ., graduate school of math., ass.prof., 大学院・多元数理科学研究科, 助教授 (00229064)
SAITO Shuji Nagoya Univ., graduate school of math., prof., 大学院・多元数理科学研究科, 教授 (50153804)
OCHIAI Hiroyuki Kyushu Univ., graduate school of math.sci., ass.prof., 大学院・数理学研究科, 助教授 (90214163)
UZAWA Tohru Rikkyo Univ., dept.of math., ass.prof., 理学部, 助教授 (40232813)
MUKAI Shigeru Nagoya Univ., graduate school of math., prof., 大学院・多元数理科学研究科, 教授 (80115641)
SAITO Takeshi Univ.of Tokyo, graduate school of math.sci., prof., 大学院・数理科学研究科, 教授 (70201506)
|Project Period (FY)
1998 – 2000
Completed(Fiscal Year 2000)
|Budget Amount *help
¥3,300,000 (Direct Cost : ¥3,300,000)
Fiscal Year 2000 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1999 : ¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 1998 : ¥1,400,000 (Direct Cost : ¥1,400,000)
|Keywords||Galois representation / non-commutative class field theory / automorphic form / automorphic representation / Iwasawa theory / 岩澤理論 / 岩澤-Greenberg 予想 / 円分体 / ヘッケ環 / 岩沢加群 / 岩沢主予想|
The notion of Taylor-Wiles system was born by analyzing a partial anwer to the Taniyama-Shimura conjecture on elliptic curves. This new axiomatic approach as well as Euler system is becoming a basic tool in Iwasawa theory. During this research period, Taylor-Wiles system approaches have been developed in the following directions :
a) R=T theorems for Hida's nearly ordinary Hecke algebras,
b) Study of cyclotomic towers of totally real fields,
c) Construction of Taylor-Wiles systems for higher dimensional unitary Shimura varieties.
In a), it is shown that nearly ordinary Hecke algebras defined by H.Hida (UCLA) corresponding to residually irreducible representations are identified with universal deformation rings in almost all cases.
In b), I have formulated a non-abelian version of Iwasawa-Greenberg conjecture.
To study this problem, a deformation theory over cyclotomic tower is developed. For special 2-dimensional representations, it is found that this new problem is equivalent to the classical Iwasawa-Greenberg conjecture by the technique of Taylor-Wlles systems. This result was announced at the international conference on automorphic forms at CEB (Paris, France) in April 2000.
In c), Taylor-Wiles systems are constructed for the canonical integral structure of the cohomology groups. The result is announced at the international workshop "Algebraic Geometry 2000" (July 2000, Nagano, Japan), the third Asian Congress of Mathematicians (Oct. 2000, Manila, Philippine), and the international workshop "Automorphic forms and Shimura varieties" (March 2001, Baltimore, USA).
Besides these oral communications, these results are distributed in a preprint form, and submitted to Journals.