OZAKI Manabu 尾崎学

Researcher Number	80287961
Other IDs
External Links
Affiliation (Current)	2022: 早稲田大学, 理工学術院, 教授
Affiliation (based on the past Project Information) *help	2011 – 2022: 早稲田大学, 理工学術院, 教授 2010: 近畿大学, 理工学部, 教授 2007 – 2009: Kinki University, 理工学部, 准教授 2005 – 2006: 近畿大学, 理工学部, 助教授 2001 – 2004: 島根大学, 総合理工学部, 助教授 … More 1998 – 2000: 島根大学, 総合理工学部, 講師 1999: Waseda Univ. School of Sci. and Eng., Assistant, 理工学部, 助手(平9) 1997: 早稲田大学, 理工学部, 助手 Less
Review Section/Research Field	Principal Investigator Algebra / Algebra / Basic Section 11010:Algebra-related Except Principal Investigator Algebra / Algebra
Keywords	Principal Investigator 岩澤理論 / ガロワ群 / 代数的整数論 / Galois群 / 非アーベル拡大 / Z_p-拡大 / 不分岐拡大 / 代数体 / 岩澤不変量 / イデアル類群 … More / 制限分岐拡大 / 最大不分岐拡大 / 岩澤加群 / 算術的同値 / 絶対Galois群 / Neukirch-内田の定理 / Greenberg予想 / 円分体 / 非アーベルp-拡大 / 非アーベル数論 / 最大不分岐p-拡大 / 非アーベル拡大の数論 / 数論 / デデキントゼータ函数 / 単数群 / ガロワコホモロジー / 馴分岐拡大 / Dedekindゼータ函数 / 非Abel拡大 / 全円分拡大 … More Except Principal Investigator 半群 / 岩沢不変 / 群 / 融合問題 / 語の問題 / アルゴリズム / semigroup / 融合 / ファイバー / ホモトピー / レトラクト / 自由融合積 / homotopy / 不値環 / 楕円曲線 / モジュラー曲線 / 谷山-志村予想 / ヤコビ多様体 / モジュラー形式 / アーベル多様体 / 代数曲線 / Q-curve / modularity / アーベル曲面 / Q-曲線 / テータ級数 / 保型形式 / elliptic curves / modular curves / Taniyama-Simura Conjecture / jacobian variety / modular forms / abelian varieties / algebraic curvers / Q-curves / 一般化された逆半群 / 論理プログラミング / レトアクト / 組合せ / membership問題 / amalgamation / generalized *-semigroup / Fiber / Logic programming / Retract / Iwasawa invariant / 書き換えシステム / 計算論理 / 岩沢変換 / メンバーズシップ問題 / amalgam / algorithm / fibre / rewriting system / caluculus / Iwasawa theory / 位相空間 / フィアバー・ホモトピー / λ計算 / 付値環 / 岩沢加群 / 羊群 / 融合積 / 書換えシステム / group / amalgamation Problem / topological space / Fibre homotopy / λcalculus / valuation ring / Iwakawa module Less

全円分拡大の岩澤理論構築への挑戦Principal Investigator
- Principal Investigator
  
  尾崎学
- Project Period (FY)
  2022 – 2025
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11010:Algebra-related
- Research Institution
  Waseda University
非アーベル岩澤理論の新展開Principal Investigator
- Principal Investigator
  
  尾崎学
- Project Period (FY)
  2019 – 2022
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11010:Algebra-related
- Research Institution
  Waseda University
Iwasawa theoretic approach to the absolute Galois groups of number fieldsPrincipal Investigator
- Principal Investigator
  
  Ozaki Manabu
- Project Period (FY)
  2016 – 2019
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Waseda University
Non-abelian extensions of number fields with restricted ramificationPrincipal Investigator
- Principal Investigator
  
  Ozaki Manabu
- Project Period (FY)
  2013 – 2016
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Waseda University
Study of non-abelian number theory based on Iwasawa theoryPrincipal Investigator
- Principal Investigator
  
  OZAKI Manabu
- Project Period (FY)
  2009 – 2012
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Waseda University
  Kinki University
Development of non-abelian Iwasawa theoryPrincipal Investigator
- Principal Investigator
  
  OZAKI Manabu
- Project Period (FY)
  2006 – 2008
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Algebra
- Research Institution
  Kinki University
非アーベル岩澤理論の研究Principal Investigator
- Principal Investigator
  
  尾崎学
- Project Period (FY)
  2003 – 2005
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Algebra
- Research Institution
  Kinki University
  Shimane University
Combinatorial semigroup theory and its applications
- Principal Investigator
  
  SHOJI Kunitaka
- Project Period (FY)
  2003 – 2004
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Shimane University
代数体の岩澤理論の非アーベルp-拡大の手法による研究Principal Investigator
- Principal Investigator
  
  尾崎学
- Project Period (FY)
  2001 – 2002
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Algebra
- Research Institution
  Shimane University
Combinatorial semigroup theory and its applications
- Principal Investigator
  
  SHOJI Kunitaka
- Project Period (FY)
  2001 – 2002
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Shimane University
Combinatorial semigroup theory and its applications
- Principal Investigator
  
  SHOJI Kunitaka
- Project Period (FY)
  1999 – 2000
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Shimane University
有理数体の総実p-拡大体に対するGreenberg予想の研究Principal Investigator
- Principal Investigator
  
  尾崎学
- Project Period (FY)
  1998 – 1999
- Research Category
  
  Grant-in-Aid for Encouragement of Young Scientists (A)
- Research Field
  
  Algebra
- Research Institution
  Shimane University
Research on the arithmetic of algebraic curves and jacobian varieties
- Principal Investigator
  
  HASHIMOTO Kiichiro
- Project Period (FY)
  1997 – 1999
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Waseda University

All 2017 2016 2015 2014 2013 2011 2010 2009 2008 2007 2006 2005 2004 Other

All Journal Article Presentation

[Journal Article] Non-abelian Iwasawa theory of Z_p-extensions---overview and outlook. (Japanese)2017
- Author(s)
  Manabu Ozaki
- Journal Title
  
  RIMS Kokyuroku Bessatsu,
  
  Volume: B64 Pages: 313-330
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-16K05080
[Journal Article] GCD LCM-like identities for ideals in commutative rings2016
- Author(s)
  Daniel D. Anderson, Shuzo Izumi, Yasuo Ohno and Manabu Ozaki
- Journal Title
  
  . J. Algebra Appl.
  
  Volume: 印刷中 Pages: 1-12
- DOI
  10.1142/s0219498816500109
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-23540036, KAKENHI-PROJECT-15K04774, KAKENHI-PROJECT-25400028
[Journal Article] On the Iwasawa λ-invariant of the cyclotomic Z_2-extension of Q(√p) , III2016
- Author(s)
  Fukuda, Takashi; Komatsu, Keiichi; Ozaki, Manabu; Tsuji, Takae
- Journal Title
  
  Funct. Approx. Comment. Math.
  
  Volume: 54
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-25400028
[Journal Article] Characterization of arithmetical equivalence of number fields by Galois groups with restricted ramification2013
- Author(s)
  M.Tohkailin, M.Ozaki
- Journal Title
  
  Tokyo J. of Math.
  
  Volume: 未定
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540030
[Journal Article] On tame pro-p Galois groupsoverbasicZpextensions2013
- Author(s)
  Y.Mizusawa, M.Ozaki
- Journal Title
  
  Mathematische Zeitschrift
  
  Volume: 273 Pages: 1161-1173
- DOI
  10.1007/s00209-012-1048-2
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540030, KAKENHI-PROJECT-22740010
[Journal Article] On tame pro-p Galois groups over basic Zp-extensions2013
- Author(s)
  Y.Mizusawa, M.Ozaki
- Journal Title
  
  Mathematische Zeitschrift
  
  Volume: 273 Pages: 1161-1173
- Data Source
  KAKENHI-PROJECT-21540030
[Journal Article] Construction of maximal unramified p-extensions with prescribed Galois groups2011
- Author(s)
  M. Ozaki
- Journal Title
  
  Invent. Math.
  
  Volume: 183 Pages: 649-680
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540030
[Journal Article] Construction of maximal unramified p-extensions with prescribed Galois groups2011
- Author(s)
  尾崎学
- Journal Title
  
  Inventiones Mathematicae
  
  Volume: 183 Pages: 649-680
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540030
[Journal Article] Remark on the Iwasawa invariants of p-extensions of a totally real number field2010
- Author(s)
  尾崎学
- Journal Title
  
  Interdisciplinary Information Sciences
  
  Volume: 16 Pages: 67-70
- NAID
  130000250322
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540030
[Journal Article] Abelian class field towers over the cyclotomic Z_2-extensions of imaginary quadratic fields2010
- Author(s)
  尾崎学, 水澤靖
- Journal Title
  
  Mathematische Annalen
  
  Volume: 347 Pages: 437-453
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540030
[Journal Article] Construction of real abelian fields of degree $p$ with λ_p=μ_p=02009
- Author(s)
  尾崎学
- Journal Title
  
  Int.J.Open Probl.Comput.Sci.Math. 2
  
  Pages: 342-351
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540030
[Journal Article] Non-abelian Iwasawa theory of Z_p-extensions2007
- Author(s)
  尾崎学
- Journal Title
  
  Journal fur die reine und angewandte Mathematik 602
  
  Pages: 59-94
- Data Source
  KAKENHI-PROJECT-18740019
[Journal Article] Construction of Z_p-extensions with prescribed Iwasawa λ-invariants2006
- Author(s)
  尾崎学, 大木義博, 藤井俊
- Journal Title
  
  Journal of Number Theory 118・2
  
  Pages: 200-207
- Data Source
  KAKENHI-PROJECT-18740019
[Journal Article] Construction of maximal unramified p-extensions with prescribed Galois group2006
- Author(s)
  尾崎学
- Journal Title
  
  数理解析研究所講究録 1521
  
  Pages: 150-155
- Data Source
  KAKENHI-PROJECT-18740019
[Journal Article] 虚2次体の円分Z2拡大上の可換2-類体塔2005
- Author(s)
  水澤靖, 尾崎学
- Journal Title
  
  京都大学数理解析研究所講究録 1451
  
  Pages: 225-232
- Data Source
  KAKENHI-PROJECT-15740016
[Journal Article] Construction of Z_p-extensions with prescribed Iwasawa modules.2004
- Author(s)
  尾崎学
- Journal Title
  
  J. of Math.Soc.Japan 56
  
  Pages: 787-801
- NAID
  10013358953
- Data Source
  KAKENHI-PROJECT-15740016
[Journal Article] Construction of Z_p-extensions with prescribed Iwasawa modules2004
- Author(s)
  Manabu Ozaki
- Journal Title
  
  J.Math.Soc.Japan 56
  
  Pages: 787-801
- NAID
  10013358953
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-15540029
[Journal Article] Construction of Z_Ρ-extensions with prescribed Iwasawa modules2004
- Author(s)
  Manabu Ozaki
- Journal Title
  
  J.Math.Soc.Japan 56
  
  Pages: 787-801
- Data Source
  KAKENHI-PROJECT-15540029
[Journal Article] the Z_p-ranks of Tamely Ramified Iwasawa Modules
- Author(s)
  Y.Mizusawa, T.Itoh, M.Ozaki
- Journal Title
  
  Int. J .Number Theory
  
  Volume: (掲載決定)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540030
[Journal Article] Construction of abelian fields of degree p with λ_p=μ_p=0
- Author(s)
  尾崎学
- Journal Title
  
  Int. J. Open Probl. Comput. Sci. Math (掲載予定)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18740019
[Journal Article] Characterization of arithmetical equivalence of number fields by Galois groups with restricted ramification
- Author(s)
  M.Tohkailin, M.Ozaki
- Journal Title
  
  Tokyo J. Math.
  
  Volume: (掲載決定)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21540030
[Journal Article] Construction of Z_p-extensions with prescribed Iwasawa λ - invariants
- Author(s)
  大木義博, 藤井俊, 尾崎学
- Journal Title
  
  J.Number Theory (掲載予定)
- Data Source
  KAKENHI-PROJECT-15740016
[Journal Article] Non-abelian Iwasawa theory of Z_p-extensions
- Author(s)
  尾崎学
- Journal Title
  
  J.Reine Angew.Math. (掲載予定)
- Data Source
  KAKENHI-PROJECT-15740016
[Presentation] ある種の無限次代数体の絶対Galois群について2016
- Author(s)
  尾崎　学
- Organizer
  北陸数論研究集会2016
- Place of Presentation
  金沢大学サテライトプラザ
- Invited
- Data Source
  KAKENHI-PROJECT-16K05080
[Presentation] 無限次代数体に対する Neukirch - 内田の定理2015
- Author(s)
  尾崎学
- Organizer
  早稲田大学整数論研究集会
- Place of Presentation
  早稲田大学
- Year and Date
  2015-03-19
- Invited
- Data Source
  KAKENHI-PROJECT-25400028
[Presentation] 代数体の付随するガロワ群による特徴付けについて2014
- Author(s)
  尾崎　学
- Organizer
  代数学シンポジウム
- Place of Presentation
  東京大学数理科学研究科
- Invited
- Data Source
  KAKENHI-PROJECT-25400028
[Presentation] The Neukirch-Uchida theorem for a certain class of number fields of infinite degree2014
- Author(s)
  尾崎　学
- Organizer
  早稲田大学整数論研究集会
- Place of Presentation
  早稲田大学理工学術院
- Data Source
  KAKENHI-PROJECT-25400028
[Presentation] 代数体の付随するガロワ群による特徴付けについて2014
- Author(s)
  尾崎学
- Organizer
  代数学シンポジウム
- Place of Presentation
  東京大学
- Year and Date
  2014-09-10
- Data Source
  KAKENHI-PROJECT-25400028
[Presentation] 無限次代数体に対するNeukirch-内田の定理について2013
- Author(s)
  尾崎　学
- Organizer
  北陸数論セミナー
- Place of Presentation
  金沢大学
- Invited
- Data Source
  KAKENHI-PROJECT-25400028
[Presentation] On the abelian groups which occur as Galois cohomology groups of global unit groups2013
- Author(s)
  尾崎学
- Organizer
  Number theory forlum
- Place of Presentation
  慶應大学
- Invited
- Data Source
  KAKENHI-PROJECT-21540030
[Presentation] On the Neukirch-Uchida theorem for certain number fields of infinite degree.2013
- Author(s)
  尾崎　学
- Organizer
  Aterier pro-p groupes et arithmetique
- Place of Presentation
  Universite de Franche-Comte, (France)
- Invited
- Data Source
  KAKENHI-PROJECT-25400028
[Presentation] On the abelian groups which occur as Galois cohomology groups of global unit groups2013
- Author(s)
  尾崎学
- Organizer
  Number theory forlum
- Place of Presentation
  慶應義塾大学
- Year and Date
  2013-03-25
- Data Source
  KAKENHI-PROJECT-21540030
[Presentation] Construction of maximal unramified p-extensions with prescribed Galois group2008
- Author(s)
  尾崎学
- Organizer
  日韓整数論セミナー2008
- Place of Presentation
  東北大学
- Year and Date
  2008-11-13
- Data Source
  KAKENHI-PROJECT-18740019
[Presentation] 与えられたp-群をガロワ群に持つ最大不分岐p-拡大の構成2008
- Author(s)
  尾崎学
- Organizer
  第13回早稲田大学整数論研究集会
- Place of Presentation
  早稲田大学
- Year and Date
  2008-03-12
- Data Source
  KAKENHI-PROJECT-18740019
[Presentation] Construction of maximal unramified p-extensions with prescribed Galois groups2008
- Author(s)
  尾崎学
- Organizer
  Japan-Korea Joint Seminar on Number Theory and Related Topics 2008
- Place of Presentation
  東北大学
- Year and Date
  2008-11-13
- Data Source
  KAKENHI-PROJECT-18740019
[Presentation] 与えられたp-群をガロワ群に持つ最大不分岐p-拡大の構成2007
- Author(s)
  尾崎学
- Organizer
  第13回早稲田大学整数論研究集会
- Place of Presentation
  早稲田大学
- Year and Date
  2007-03-12
- Data Source
  KAKENHI-PROJECT-18740019

1. UEDA Akira (70213345)

# of Collaborated Projects: 3 results

# of Collaborated Products: 0 results
2. SHOJI Kunitaka (50093646)

# of Collaborated Projects: 3 results

# of Collaborated Products: 0 results
3. MIWA Takuo (60032455)

# of Collaborated Projects: 3 results

# of Collaborated Products: 0 results
4. IMAOKA Teruo (60032603)

# of Collaborated Projects: 3 results

# of Collaborated Products: 0 results
5. FUJITA Kenetsu (30228994)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
6. MIZUSAWA Yasushi (60453817)

# of Collaborated Projects: 2 results

# of Collaborated Products: 4 results
7. FUJII Satoshi (20386618)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
8. KONDO Michiro (40211916)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
9. ITOH Tsuyoshi

# of Collaborated Projects: 2 results

# of Collaborated Products: 1 results
10. TOHKAILIN Mitsul

# of Collaborated Projects: 2 results

# of Collaborated Products: 2 results
11. OKANO Keiji

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
12. HASHIMOTO Kiichiro (90143370)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
13. HASEGAWA Yuji (30287982)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
14. ADACHI Norio (60063731)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
15. KOMATSU Keiichi (80092550)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
16. KAGAWA Takaaki (90298175)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
17. MAIRE Christian

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
18. ABBAS Chazad Movahhedi

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
19. BRUNO Angles

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
20. Maire C.

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
21. Movahhedi A.

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
22. Angles B.

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
23. 大野泰生

# of Collaborated Projects: 0 results

# of Collaborated Products: 1 results

OZAKI Manabu 尾崎 学

Research Projects

Research Products

Co-Researchers

全円分拡大の岩澤理論構築への挑戦Principal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

非アーベル岩澤理論の新展開Principal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

Iwasawa theoretic approach to the absolute Galois groups of number fieldsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Non-abelian extensions of number fields with restricted ramificationPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Study of non-abelian number theory based on Iwasawa theoryPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Development of non-abelian Iwasawa theoryPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

非アーベル岩澤理論の研究Principal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Combinatorial semigroup theory and its applications

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

代数体の岩澤理論の非アーベルp-拡大の手法による研究Principal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Combinatorial semigroup theory and its applications

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Combinatorial semigroup theory and its applications

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

有理数体の総実p-拡大体に対するGreenberg予想の研究Principal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Research on the arithmetic of algebraic curves and jacobian varieties

Principal Investigator

Project Period (FY)

Research Category

OZAKI Manabu 尾崎学