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Publications of Katsumi Shimomura
Last update: May, 2008
Papers

KOgroups of lens spaces modulo power of two (with K. Fujii, T. Kobayashi, and M. Sugawara), Hiroshima Math. J. 8 (1978), 469489.

Novikov's Ext^2 at the prime 2, Hiroshima Math. J. 11 (1981), 499513.

On product of the $\beta$elements in the stable homotopy of spheres (with S. Oka), Hiroshima Math. J. 12 (1982), 611626.

Nontriviality of some compositions of $\beta$elements in the stable homotopy of the Moore spaces (with H. Tamura), Hiroshima Math. J. 16 (1986), 121133.

On the AdamsNovikov spectral sequence and products of $\beta$elements, Hiroshima Math. J. 16 (1986), 209224.

BP Hopf module spectrum and BP_* Adams spectral sequence (with Z. Yosimura), Publ. RIMS, Kyoto Univ. 21 (1986), 925947.

Nontriviality of products of $\beta$elements in the stable homotopy of spheres, Hiroshima Math. J. 17 (1987), 349353.

Triviality of products of $\beta$elements in the stable homotopy group of spheres, J. Math. Kyoto Univ. 29 (1989), 5767.

On the products $\beta_s\beta_t$ in the stable homotopy groups of spheres, Hiroshima Math. J. 19 (1989), 347354.

A spectrum whose BP_* homology is (BP_*/I_5)[t_1], Hiroshima Math. J. 21 (1991), 587595.

On some products of $\beta$elements in the homotopy of the Moore spectrum (with M. Mabuchi), Math. J. Okayama Univ. 34 (1992), 195204.

The AdamsNovikov spectral sequence for the L_2 localization of a v_2 spectrum (with M. Mahowald), the Proceedings of the International Congress in Algebraic Topology, Editated by M. Tangora, 1991, Contemporary Math. 146, (1993), 237250.

On the chromatic E_1term H^*M_0^2 (with A. Yabe),
Topology and Representation Theory, Contemporary Math. 158,
(1994), 217228.

Existence of the greek letter elements in the stable homotopy groups of E(n)_*localized spheres (with M. Yokotani), Publ. RIMS, Kyoto Univ. 30 (1994), 139150.

An exact sequence related to AdamsNovikov E_2term of a cofibering (with M. Hikida), J. Math. Soc. of Japan 46 (1994), 645661.

On some products of $\beta$elements in the homotopy of the Moore spectrum II (with H. Inoue and Y. Osakada), Okayama Math. J. 36 (1994), 185197.

The homotopy groups $\pi_*(L_2S^0)$ (with A. Yabe),
Topology 34 (1995), 261289.

On products of $\beta$elements in the homotopy of L_2local spheres (with R. Otsubo), Kodai Math. J. 18 (1995), 234241.

The products $\beta_s\beta_{tp/p}$ in the stable homotoy of L_2localized spheres,
Hiroshima Math. J. 25 (1995), 487491.

The homotopy groups of the L_2localized Mahowald spectrum X<1>, Forum Math. 7 (1995), 685707.

The homotopy groups of a spectrum whose BP_* homology is v_2^{1}BP_*/(2)[t_1]\otimes \La(t_2) (with K. Masamoto and T. Matsuhisa), Osaka J. Math. 33 (1996), 6982.

3primary $\beta$family in stable homotopy of a finite spectrum,
Hiroshima Math. J. 26 (1996), 341349.

The chromatic E_1term H^1M_1^1 at the prime 3 (with Y. Arita),
Hiroshima Math. J. 26 (1996), 415431.

The homotopy groups of the L_2localization of a type one finite complex at the prime 3 (with Y. Nakazawa), Fundamenta Mathematicae 152 (1997), 1 20.

The homotopy groups of L_2localized TodaSmith spectrum V(1) at the prime 3, Trans.~Amer.~Math.~Soc. 349 (1997), 18211850.

On the products of some $\beta$elements in the homotopy of the mod 3 Moore spectrum (with Y. Arita), Hiroshima Math. J. 27 (1997), 477486.

The homotopy groups of an L_2localized type one finite spectrum at the prime 2, Hiroshima Math. J. 28 (1998), 113127.

The AdamsNovikov E_2term for computing $\pi_*(L_2V(0))$ at the prime 2,
Topology and its Applications 96 (1999), 133152.

The homotopy groups of the L_2localized mod 3 Moore spectrum,
J. Math. Soc. of Japan 51 (2000), 6590.

On the action of $\beta_1$ in the stable homotopy of spheres at the prime 3,
Hiroshima Math. J. 30 (2000), 345362.

The homotopy groups $\pi_*(L_2V(0)\wedge T(k))$ , Hiroshima Math. J. 31 (2001), 391408. (with Y. Kamiya)

The homotopy groups $\pi_*(L_2S^0)$ at the prime 3 , Topology 41 (2002), 11831198. (with X. Wang)
ERRATA

The homotopy groups $\pi_*(L_nT(m)\wedge V(n2))$ , Contemp. Math. 293 (2002), 285297.

The AdamsNovikov E_2term for $\pi_*(L_2S^0)$ at the prime 2 , Math. Z. 241 (2002), 271311.(with X. Wang)

E_*homology spheres for a connected spectrum E, Contemp. Math. 314 (2002), 153159. (with Y. Kamiya)

On the homotopy groups of an invertible spectrum in the $E(2)$local category at the prime 3, JP Jour. Geometry & Topology 3 (2003), 257268. (with I. Ichigi)

Subgroups of $\pi_*(L_2T(1))$ at the prime two, Hiroshima Math. J. 33 (2003), 359369. (with I. Ichigi)

A relation between the Picard groups of the $E(n)$local homotopy category and $E(n)$based Adams spectral sequence, Contemp. Math. 346 (2004), 321333.(with Y. Kamiya)

$E(2)_*$invertible spectra smashing with the SmithToda spectrum $V(1)$ at the prime 3
, Proc. Amer. Math. Soc. 132 (2004), 31113119. (with I. Ichigi)

Homotopy groups of a generalized $E(2)$local Moore spectrum at the prime three, Hiroshima Math. J. 35 (2005), 125142. (with I. Ichigi)

On the homotopy groups of $E(n)$local spectra with unusual invariant ideals, Geometry & Topology Monographs 10 (2007) 319332
(with H. Nakai)

Picard groups of some local categories, Publ. RIMS, Kyoto Univ. 432 (2007), 303314. (with Y. Kamiya)

On subgroups of $\pi_*(L_2T(1)\wedge M(2))$ at the prime two, Bol. Soc. Mat. Mexicana. vol. 131, (2007), 207230 (with I. Ichigi and X. Wang)

The modulo two homotopy groups of the $L_2$localization of the Ravenel spectrum, Cubo Math. J. 103 (2008), 4355.
(with I. Ichigi)

The homotopy groups of the $L_2$localization of the modulo $p$ Moore spectrum smashing with the first Ravenel spectrum, AsianEuropean Journal of Mathematics, Vol.31(2010), 107118. (with I. Ichigi)

The homotopy groups of L_2localization of the Ravenel spectra T(m)/v_1 at the prime two, Bulletin of the Mexican Mathematical Society, 161 (2010), 5362.(with I. Ichigi and R. Takeda)

Note on beta elements in homotopy, and an application to the prime three case, Proc. Amer. Math. Soc. 138 (2010), 14951499

The beta elements $\be_{tp^2/r}$ in the homotopy of spheres, Algebraic and Geometric Topology 10 (2010) 20792090.

On the chromatic $Ext^0(M^1_{n1})$ on $\Gamma(m+1)$ for an odd prime, Hiroshima Math. J. 41 (2011), 211222.
(with R. Kitahama)

The cohomology of $S(n,n1)$ relevant to the Morava stabilizer algebra at an odd prime, Kochi Journal of Mathematics 7 (2012), 109118.
(with S. Tokashiki)

Products of greek letter elements dug up from
the third morava stabilizer algebra, Algebraic and Geometric Topology 12 (2012), 951961.
(with R. Kato)

The first line of the Bockstein spectral sequence
on a monochromatic spectrum at an odd prime, Nagoya Mathematical Journal 207 (2012), 139157.
(with R. Kato)

A beta family in the homotopy of spheres, Proceedings of the American Mathematical Society 142 (2014), 292128.

On the product $\alpha_1\beta_1^r\gamma_t$ in the stable homotopy groups of spheres, Kochi Journal of Mathematics 9 (2014), 169172. (with K. Yoshizawa)

Generalized Bousfield lattices and a generalized
retract conjecture, Publ. RIMS. Kyoto Univ. 503(2014), pp. 497513. (with R. Kato and Y. Tatehara)

A note on the products $\alpha_1\beta_1^r\beta_2\gamma_t$ and $\beta_1^{r+1}\beta_2\gamma_t$ in the stable homotopy of spheres,
Hiroshima Math. J. 49(3) (2019), 303321. (with H. Okajima)

A note on Hopkins' Picard groups of the stable homotopy categories of $L_{n}$local spectra,
Publ. RIMS. Kyoto Univ. 561(2020), 195205

Notes on an algebraic stable homotopy category,
Bousfield classes and Ohkawa's theorem:Nagoya, Japan, August 2830, 2015, Springer Proc. Math. Stat., 309, 2020, 103108. (with R. Kato and H. Okajima)

A note on products in stable homotopy groups of spheres via the classical Adams spectral sequence,
Math. J. Okayama Univ. 63(2021), 107122. (with R. Kato)

On the Picard group graded homotopy groups of a finite type two $K(2)$local spectrum at the prime three,
Homology, Homotopy and Applications, 24(1) (2022), 177203. (with I. Ichigi)

A relation among Hopkins' Picard groups of the localized categories with respect to finite wedges of the Morava $K$theories,
Trans. Amer. Math. Soc. 375 (2022), 63376361

Beta families arising from a $v_2^9$ self map on $S/(3,v_1^8)$, Algebraic & Geometric Topology 23:9 (2023), 43494378 (with E. Belmont)

On products of beta and gamma elements in the homotopy of the first SmithToda spectrum, to appear in Algebraic & Geometric Topology (with M. Shimomura)
Papers (Kiyo et al)

Note on invariant regular ideals in BP_* , J. Fac. Educ. Tottori Univ. (Nat. Sci.) 37 (1988), 103110.

Invariant regular sequences in the BrownPeterson homology BP_* (with C. Takamura), J. Fac. Educ. Tottori Univ. (Nat. Sci.) 38 (1989), 6775.

Note on the right unit map and some elements of the BrownPeterson homology, J. Fac. Educ. Tottori Univ. (Nat. Sci.) 38 (1989), 7789.

Computation of obstruction for a spectrum with BP_* homology (BP_*/I_n)[t_1,t_2,...,t_k] (with A. Yabe), J. Fac. Educ. Tottori Univ. (Nat. Sci.) 39 (1990), 8594.

The chromatic E_1term H^1M^1_2 and its application to the homology of the TodaSmith spectrum V(1), J. Fac. Educ. Tottori Univ. (Nat. Sci.) 39 (1990), 6383.
Corrections to ``The chromatic E_1term H^1M^1_2 and its application to the homology of the TodaSmith spectrum V(1)'', J. Fac. Educ. Tottori Univ. (Nat. Sci.) 41 (1992), 711.

The chromatic E_1term H^0M^2_n for n> 1, J. Fac. Educ. Tottori Univ. (Nat. Sci.) 39 (1990), 103121.

On the 2nd obstruction on the existence of the TodaSmith V(4), J. Fac. Educ. Tottori Univ. (Nat. Sci.) 40 (1991), 16.

On the E_2term of the Novikov spectral sequence for a Thom spectrum, J. Fac. Educ. Tottori Univ. (Nat. Sci.) 40 (1991), 2532.

Note on the Bousfield localization with respect to E(n), J. Fac. Educ. Tottori Univ. (Nat. Sci.) 41 (1992), 15.

On differential of a generalized Adams spectral sequence,
J. Fac. Educ. Tottori Univ. (Nat. Sci.) 41 (1992), 119131.

Homotopy groups of L_2localized sphere (with A. Yabe), 代数的トポロジーの発展と展望研究集会報告集, 数理解析研究所講究録 838 , 934.

A generalized Adams spectral sequence based on a BP associated spectrum,
J. Fac. Educ. Tottori Univ. (Nat. Sci.) 42 (1993), 115.

On the homotopy groups of a spectrum related to Ravenel's spectra T(n) (with N. Kodama),
J. Fac. Educ. Tottori Univ. (Nat. Sci.) 42 (1993), 1730.

The Ext groups H^0M_2^1(1) (with H. Mitsui),
J. Fac. Educ. Tottori Univ. (Nat. Sci.) 42 (1993), 85101.

The homotopy groups of some L_nlocal spectra (with R. Otsubo), J. Fac. Educ. Tottori Univ. (Nat. Sci.) 43 (1994), 16.

A note on the chromatic convergence theorem, J. Fac. Educ. Tottori Univ. (Nat. Sci.) 43 (1994), 1520.

Chromatic E_1terms  up to April 1995,
J. Fac. Educ. Tottori Univ. (Nat. Sci.) 44 (1995), 16.

On a stable homotopy of a spectrum at the prime 3,
J. Fac. Educ. Tottori Univ. (Nat. Sci.) 44 (1995), 711.

Realization of a subalgebra of a generalized Steenrod algebra,
J. Fac. Educ. Tottori Univ. (Nat. Sci.) 44 (1995), 103110.
 A novice's guide to calculation of the Bockstein spectral sequences, J. Fac. Educ. Tottori Univ. (Nat. Sci.) 45 (1996), 124.

Note on a relation between the stick number and the minimum crossing number of a knot (with Y. Kishima), J. Fac. Educ. Tottori Univ. (Nat. Sci.) 45 (1996), 2534.

Note on the $\beta$ family in the homotopy of spheres, J. Fac. Educ. Tottori Univ. (Nat. Sci.) 45 (1996), 103110.

The chromatic E_1term Ext^0(v_3^{1}BP_*/(3,v_1,v_2^\infty)[t_1]) (with I. Ichigi),
Mem. Fac. Sci. Kochi Univ. Ser. A (Math.) 21 (2000), 6371.
Preprints

The homotopy groups of $L_2V(1\frac 12)$ and an invertible spectrum at the prime three, preprint. (with I. Ichigi)

The $\beta_{9t+3}$ in stable homotopy of spheres at the prime 3, preprint.

Picard group of the $E(2)$local stable homotopy category at the prime three, preprint.

A beta family in the homotopy of spheres, preprint.
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