Murakami, Kazuaki

写真a

Affiliation

Affiliated Schools, Keio Girls Senior High School (Mita)

Position

Teacher

Other Affiliation 【 Display / hide

  • Graduate School of Science and Engineering, Department of Mathematical Sciences , 訪問研究員

Academic Degrees 【 Display / hide

  • 博士 (理学), Keio University, Coursework, 2015.09

 

Research Areas 【 Display / hide

  • Algebra (Number Theory)

Research Keywords 【 Display / hide

  • Number Theory

Research Themes 【 Display / hide

  • Iwasawa Theory, 

    2009
    -
    Present

 

Papers 【 Display / hide

  • Weak Greenberg's generalized conjecture for imaginary quadratic fields

    Kazuaki Murakami

     2020.10

    Research paper (scientific journal), Single Work

     View Summary

    Let $p$ be an odd prime number and $k$ an imaginary quadratic field in which
    $p$ splits. In this paper, we consider a weak form of Greenberg's generalized
    conjecture for $p$ and $k$, which states that the non-trivial Iwasawa module of
    the maximal multiple $\mathbb{Z}_p$-extension field over $k$ has a non-trivial
    pseudo-null submodule. We prove this conjecture for $p$ and $k$ under the
    assumption that the Iwasawa $\lambda$-invariant for a certain
    $\mathbb{Z}_p$-extension over a finite abelian extension of $k$ vanishes and
    that the characteristic ideal of the Iwasawa module associated to the
    cyclotomic $\mathbb{Z}_p$-extension over $k$ has a square-free generator.

  • Galois coinvariants of the unramified Iwasawa modules of multiple Zp-extensions

    Takashi Miura, Kazuaki Murakami, Keiji Okano, and Rei Otsuki

    Annales mathématiques du Québec (Springer)     1 - 25 2020

    Research paper (scientific journal), Joint Work, Accepted

  • On a new invariant determining the isomorphism classes of Λ -modules with λ= 3

    Kazuaki Murakami

    Manuscripta Mathematica (Springer)   2020

    Research paper (scientific journal), Single Work, Accepted,  ISSN  00252611

     View Summary

    © 2020, Springer-Verlag GmbH Germany, part of Springer Nature. For a prime number p and the ring of power series Λ = Zp[[T]] , we define a new invariant which determines the isomorphism classes of finitely generated torsion Λ -modules with λ= 3. We apply this result to the classical Selmer group attached to an elliptic curve over Q.

  • On an upper bound of λ-invariants of Zp-extensions over an imaginary quadratic field

    Kazuaki Murakami

    Journal of the Mathematical Society of Japan (Journal of the Mathematical Society of Japan)  71 ( 3 ) 1005 - 1026 2019

    Research paper (scientific journal), Single Work, Accepted,  ISSN  00255645

     View Summary

    © 2019 The Mathematical Society of Japan. For an odd prime number p, we give an explicit upper bound of λ-invariants for all Zp-extensions of an imaginary quadratic field k under several assumptions. We also give an explicit upper bound of λ-invariants for all Zp-extensions of k in the case where the λ-invariant of the cyclotomic Zp-extension of k is equal to 3.

  • Isomorphism Classes of Modules over Iwasawa Algebra with lambda=4

    Murakami Kazuaki

    TOKYO JOURNAL OF MATHEMATICS 39 ( 1 ) 101 - 132 2016.06

    Research paper (scientific journal), Single Work, Accepted,  ISSN  0387-3870

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Papers, etc., Registered in KOARA 【 Display / hide

Reviews, Commentaries, etc. 【 Display / hide

  • On the cyclicity of the unramified Iwasawa modules of the maximal multiple Zp -extensions over imaginary quadratic fields

    福岡数論研究集会報告集  2019

    Introduction and explanation (scientific journal), Single Work

  • 虚二次体上の Zp-拡大における λ 不変量の振る舞いについて

    Kazuaki Murakami

    早稲田大学整数論研究集会報告集  2018

    Introduction and explanation (scientific journal), Single Work

  • λ-不変量が 3 である岩澤加群の同型類を決定する新しい不変量について

    Kazuaki Murakami

    福岡数論研究集会報告集  2018

    Introduction and explanation (scientific journal), Single Work

  • 深谷-加藤の補題と 1 次元コンパクト p 進リー群への帰着

    Kazuaki Murakami

    第22回 (2014年度) 整数論サマースクール報告集「非可換岩澤理論」  2016

    Introduction and explanation (scientific journal), Single Work

Presentations 【 Display / hide

  • 虚二次体における弱一般 Greenberg 予想について

    Kazuaki Murakami

    代数的整数論とその周辺 (京都大学数理解析研究所) , 2020.12, Oral Presentation(general), 京都大学数理解析研究所

  • 弱一般 Greenberg 予想について

    Kazuaki Murakami

    神楽坂代数セミナー (東京理科大学理学部) , 2020.02, Oral Presentation(general), 東京理科大学

  • 一般 Greenberg 予想について

    Kazuaki Murakami

    東京理科大学理工学部 (東京理科大学理工学部) , 2019.12, Oral Presentation(general), 東京理科大学

  • On the cyclicity of the unramified Iwasawa modules of the maximal multiple Zp-extensions over imaginary quadratic fields

    Kazuaki Murakami

    福岡数論研究集会 (九州大学) , 2019.08, Oral Presentation(general), 九州大学

  • On the cyclicity of the unramified Iwasawa modules of the maximal multiple Zp-extensions over imaginary quadratic fields

    Kazuaki Murakami

    広島仙台整数論集会 (広島大学) , 2019.07, Oral Presentation(general), 広島大学

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Memberships in Academic Societies 【 Display / hide

  • 日本数学会, 

    2017
    -
    Present