■ 氏名
下村 克己 (シモムラ カツミ)
SHIMOMURA Katsumi

■ 所属部局/職名
Research and Education Faculty, Natural Sciences Cluster, Science and Technology Unit/Professor
教育研究部 自然科学系 理工学部門/教授

■ 学部・学科・コース等
Faculty of Science, Department of Natural Science, Mathematics Course
理学部 理学科 数学コース

■ 連絡先
住 所
電 話088-844-8266
F A X
E-Mailkatsumi●kochi-u.ac.jp    (送信の際は“●”を半角の“@”に変更して送信してください。)
U R Lhttp://www.math.kochi-u.ac.jp/katsumi/index.html

■ 出身大学院・研究科等
広島大学 博士(理学研究科 数学) 1984 ()

■ 出身学校・専攻等
愛媛大学 (理学部 数学) 1976 ()

■ 取得学位
理学博士 (課程)

■ 研究職歴
1988-1991 鳥取大学教育学部 講師
1992-1997 鳥取大学教育学部 助教授
1997-2000 高知大学理学部 助教授


■ 委員歴・役員歴

■ 受賞学術賞

■ 所属学会
日本数学会
 ( 国内)
American Mathematical Society(米国数学会)
 ( 国外)

■ 専門分野
ホモトピー論

■ 主な研究テーマ・活動
安定ホモトピー論、球面のホモトピー群

■ 研究についてのPR
安定ホモトピー群を決定するという見地から安定ホモトピー圏の構造を解析している。

■ 社会人・生徒を対象として可能な講演・授業(例えば講演題目)
球面のホモトピー群

■ 研究業績(論文・解説)
$KO$-groups of lens spaces modulo power of two
 Hiroshima Math. J. () 8/, 469--489 1978 (学術雑誌)

Novikov's Ext$^2$ at the prime 2
 Hiroshima Math. J. () 11/, 499--513 1981 (学術雑誌)

On product of the $\beta$-elements in the stable homotopy of spheres
 Hiroshima Math. J. () 12/, 611--626 1982 (学術雑誌)

Non-triviality of some compositions of $\be$-elements in the stable homotopy of the Moore spaces
 Hiroshima Math. J. () 16/, 121--133 1986 (学術雑誌)

On the Adams-Novikov spectral sequence and products of $\be$-elements
 Hiroshima Math. J. () 16/, 209--224 1986 (学術雑誌)

$BP$-Hopf module spectrum and $BP_*$-Adams spectral sequence
 Publ. RIMS, Kyoto Univ. () 21/, 925--947 1986 (学術雑誌)

Non-triviality of products of $\be$-elements in the stable homotopy of spheres
 Hiroshima Math. J. () 17/, 349--353 1987 (学術雑誌)

Triviality of products of $\be$-elements in the stable homotopy group of spheres
 J. Math. Kyoto Univ. () 29/, 57--67 1989 (学術雑誌)

On the products $\beta_s\beta_t$ in the stable homotopy groups of spheres
 Hiroshima Math. J. () 19/, 347--354 1989 (学術雑誌)

A spectrum whose $BP_*$-homology is $(BP_*/I_5)[t_1]$
 Hiroshima Math. J. () 21/, 587--595 1991 ()

On some products of $\be$-elements in the homotopy of the Moore spectrum
 Math. J. Okayama Univ. () 34/, 195--204 1992 (学術雑誌)

The Adams-Novikov spectral sequence for the $L_2$ localization of a $v_2$ spectrum
 Contemporary Math. () 146/, 237--250 1993 (学術雑誌)

On the chromatic $E_1$-term $H^*M_0^2$
 Contemporary Math. () 158/, 217--228 1994 (学術雑誌)

Existence of the greek letter elements in the stable homotopy groups of $E(n)_*$-localized spheres
 Publ. RIMS, Kyoto Univ. () 30/, 139--150 1994 (学術雑誌)

An exact sequence related to Adams-Novikov $E_2$-term of a cofibering
 J. Math. Soc. of Japan () 46/, 645--661 1994 (学術雑誌)

On some products of $\be$-elements in the homotopy of the Moore spectrum II
 Okayama Math. J. () 36, 185--197./, 1994 (学術雑誌)

The homotopy groups $\pi_*(L_2S^0)$
 Topology () 34, 261--289/, 1995 (学術雑誌)

On products of $\beta$-elements in the homotopy of $L_2$-local spheres
 Kodai Math. J. () 18, 234--241/, 1995 (学術雑誌)

The products $\be_s\be_{tp/p}$ in the stable homotoy of $L_2$-localized spheres
 Hiroshima Math. J. () 25, 487--491/, 1995 (学術雑誌)

The homotopy groups of the $L_2$-localized Mahowald spectrum $X<1>$
 Forum Math. () 7, 685--707/, 1995 (学術雑誌)

The homotopy groups of a spectrum whose $BP_*$-homology is $v_2^{-1}BP_*/(2)[t_1]\otimes\Lambda(t_2)$
 Osaka J. Math. () 33, 69--82/, 1996 (学術雑誌)

3-primary $\beta$-family in stable homotopy of a finite spectrum
 Hiroshima Math. J. () 26, 341--349/, 1996 (学術雑誌)

The chromatic $E_1$-term $H^1M_1^1$ at the prime 3
 Hiroshima Math. J. () 26, 415--431/, 1996 (学術雑誌)

The homotopy groups of the $L_2$-localization of a type one finite complex at the prime 3
 Fundamenta Mathematicae () 152, 1-20/, 1997 (学術雑誌)

The homotopy groups of $L_2$-localized Toda-Smith spectrum $V(1)$ at the prime 3
 Trans. Amer. Math. Soc. () 349, 1821-1850/, 1997 (学術雑誌)

On the products of some $\be$-elements in the homotopy of the mod $3$ Moore spectrum
 Hiroshima Math. J. () 27, 477-486/, 1997 (学術雑誌)

The homotopy groups of an $L_2$-localized type one finite spectrum at the prime 2
 Hiroshima Math. J. () 28, 113-127/, 1998 (学術雑誌)

The Adams-Novikov $E_2$-term for computing $\pi_*(L_2V(0))$ at the prime 2
 Topology and its Applications () 96, 133-152/, 1999 (学術雑誌)

The homotopy groups of the $L_2$-localized mod $3$ Moore spectrum
 J. Math. Soc. Japan () 51, 65-90/, 2000 (学術雑誌)

On the action of $\be_1$ in the stable homotopy of spheres at the prime 3
 Hiroshima Math. J. () 30, 345-362/, 2000 (学術雑誌)

The homotopy groups $\pi_*(L_2V(0)\wedge T(k))$
 Hiroshima Math. J. () 31, 391-408/, 2001 (学術雑誌)

The homotopy groups $\pi_*(L_nT(m)\wedge V(n-2))$
 Contemporary Math. () 293, 285-297/, 2002 (学術雑誌)

The homotopy groups $\pi_*(L_2S^0)$ at the prime $3$
 Topology () 41, 1183-1198/, 2002 (学術雑誌)

$E_*$-homology spheres for a connective spectrum $E$
 Contemporary Math. () 314, 153-159/, 2002 (学術雑誌)

The Adams-Novikov $E_2$-term for $\pi_*(L_2S^0)$ at the prime $2$
 Math. Z. () 241, 271-311/, 2002 (学術雑誌)

On the homotopy groups of an invertible spectrum in the $E(2)$-local category at the prime 3
 JP Jour. Geometry & Topology () 3, 257--268/, 2003 (学術雑誌)

Subgroups of $\pi_*(L_2T(1))$ at the prime two
 Hiroshima Math. J. () 33, 359--369/, 2003 (学術雑誌)

A relation between the Picard groups of the $E(n)$-local homotopy category and $E(n)$-based Adams spectral sequence
 Contemp. Math. () 346, 321-333/, 2004 (学術雑誌)

$E(2)_*$-invertible spectra smashing with the Smith-Toda spectrum $V(1)$ at the prime 3
 Proc. Amer. Math. Soc. () 132, 3111-3119/, 2004 (学術雑誌)

Homotopy groups of a generalized $E(2)$-local Moore spectrum at the prime three
 Hiroshima Math. J. () 35, 125--142/, 2005 (学術雑誌)

On the homotopy groups of $E(n)$-local spectra with unusual invariant ideals
 Geometry & Topology Monographs (H. Nakai and K. Shimomura) 10/, 319--332 2007 (学術雑誌)

Picard groups of some local categories
 Publ. RIMS, Kyoto Univ. (Y. Kamiya and K. Shimomura) 43/2, 303-314 2007 (学術雑誌)

On subgroups of $\pi_*(L_2T(1)\wedge M(2))$ at the prime two
 Bol. Soc. Mat. Mexicana (I. Ichigi, K. Shimomura and X. Wang) 13/1, 207--230 2007 (学術雑誌)

The modulo two homotopy groups of the $L_2$-localization of the Ravenel spectrum
 Cubo Math. J. (I. Ichigi and K. Shimomura) 10/3, 43--55 2008 (学術雑誌)

The homotopy groups of the $L_2$-localization of the modulo $p$ Moore spectrum smashing with the first Ravenel spectrum
 Asian-European Journal of Mathematics (I. Ichigi and K. Shimomura) 3/1, 107--118 2010 (学術雑誌)

Note on beta elements in homotopy, and an application to the prime three case
 Proc. Amer. Math. Soc. (K. Shimomura) 138/, 1495--1499 2010 (学術雑誌)

The beta elements $\be_{tp^2/r}$ in the homotopy of spheres
 Algebraic and Geometric Topology (K. Shimomura) 10/, 2079--2090 2010 (学術雑誌)

■ 研究業績(著書)

■ 研究業績(口頭・ポスター)

■ 研究業績(特許)

■ 研究業績(その他の活動)


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