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Publications of Katsumi Shimomura

Last update: May, 2008

Papers

Papers (Kiyo et al)

Preprints

Papers

  1. KO-groups of lens spaces modulo power of two (with K. Fujii, T. Kobayashi, and M. Sugawara), Hiroshima Math. J. 8 (1978), 469--489.
  2. Novikov's Ext^2 at the prime 2, Hiroshima Math. J. 11 (1981), 499--513. 
  3. On product of the $\beta$-elements in the stable homotopy of spheres (with S. Oka), Hiroshima Math. J. 12 (1982), 611--626.  
  4. Non-triviality of some compositions of $\beta$-elements in the stable homotopy of the Moore spaces (with H. Tamura), Hiroshima Math. J. 16 (1986), 121--133.  
  5. On the Adams-Novikov spectral sequence and products of $\beta$-elements, Hiroshima Math. J. 16 (1986), 209--224. 
  6. BP -Hopf module spectrum and BP_* -Adams spectral sequence (with Z. Yosimura), Publ. RIMS, Kyoto Univ. 21 (1986), 925--947. 
  7. Non-triviality of products of $\beta$-elements in the stable homotopy of spheres, Hiroshima Math. J. 17 (1987), 349--353. 
  8. Triviality of products of $\beta$-elements in the stable homotopy group of spheres, J. Math. Kyoto Univ. 29 (1989), 57--67.
  9. On the products $\beta_s\beta_t$ in the stable homotopy groups of spheres, Hiroshima Math. J. 19 (1989), 347--354.
  10. A spectrum whose BP_* -homology is (BP_*/I_5)[t_1], Hiroshima Math. J. 21 (1991), 587--595.
  11. On some products of $\beta$-elements in the homotopy of the Moore spectrum (with M. Mabuchi), Math. J. Okayama Univ. 34 (1992), 195--204.
  12. The Adams-Novikov 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), 237--250.
  13. On the chromatic E_1-term H^*M_0^2 (with A. Yabe), Topology and Representation Theory, Contemporary Math. 158, (1994), 217--228.
  14. 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), 139--150.
  15. An exact sequence related to Adams-Novikov E_2-term of a cofibering (with M. Hikida), J. Math. Soc. of Japan 46 (1994), 645--661.
  16. 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), 185--197.
  17. The homotopy groups $\pi_*(L_2S^0)$ (with A. Yabe), Topology 34 (1995), 261--289.
  18. On products of $\beta$-elements in the homotopy of L_2-local spheres (with R. Otsubo), Kodai Math. J. 18 (1995), 234--241.
  19. The products $\beta_s\beta_{tp/p}$ in the stable homotoy of L_2-localized spheres, Hiroshima Math. J. 25 (1995), 487--491.
  20. The homotopy groups of the L_2-localized Mahowald spectrum X<1>, Forum Math. 7 (1995), 685--707.
  21. 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), 69--82.
  22. 3-primary $\beta$-family in stable homotopy of a finite spectrum, Hiroshima Math. J. 26 (1996), 341--349.
  23. The chromatic E_1-term H^1M_1^1 at the prime 3 (with Y. Arita), Hiroshima Math. J. 26 (1996), 415--431.
  24. The homotopy groups of the L_2-localization of a type one finite complex at the prime 3 (with Y. Nakazawa), Fundamenta Mathematicae 152 (1997), 1-- 20.
  25. The homotopy groups of L_2-localized Toda-Smith spectrum V(1) at the prime 3, Trans.~Amer.~Math.~Soc. 349 (1997), 1821--1850.
  26. On the products of some $\beta$-elements in the homotopy of the mod 3 Moore spectrum (with Y. Arita), Hiroshima Math. J. 27 (1997), 477--486.
  27. The homotopy groups of an L_2-localized type one finite spectrum at the prime 2, Hiroshima Math. J. 28 (1998), 113--127.
  28. The Adams-Novikov E_2-term for computing $\pi_*(L_2V(0))$ at the prime 2, Topology and its Applications 96 (1999), 133--152.
  29. The homotopy groups of the L_2-localized mod 3 Moore spectrum, J. Math. Soc. of Japan 51 (2000), 65--90.
  30. On the action of $\beta_1$ in the stable homotopy of spheres at the prime 3, Hiroshima Math. J. 30 (2000), 345--362.
  31. The homotopy groups $\pi_*(L_2V(0)\wedge T(k))$ , Hiroshima Math. J. 31 (2001), 391--408. (with Y. Kamiya)
  32. The homotopy groups $\pi_*(L_2S^0)$ at the prime 3 , Topology 41 (2002), 1183--1198. (with X. Wang) ERRATA
  33. The homotopy groups $\pi_*(L_nT(m)\wedge V(n-2))$ , Contemp. Math. 293 (2002), 285--297.
  34. The Adams-Novikov E_2-term for $\pi_*(L_2S^0)$ at the prime 2 , Math. Z. 241 (2002), 271--311.(with X. Wang)
  35. E_*-homology spheres for a connected spectrum E, Contemp. Math. 314 (2002), 153--159. (with Y. Kamiya)
  36. On the homotopy groups of an invertible spectrum in the $E(2)$-local category at the prime 3, JP Jour. Geometry & Topology 3 (2003), 257--268. (with I. Ichigi)
  37. Subgroups of $\pi_*(L_2T(1))$ at the prime two, Hiroshima Math. J. 33 (2003), 359--369. (with I. Ichigi)
  38. A relation between the Picard groups of the $E(n)$-local homotopy category and $E(n)$-based Adams spectral sequence, Contemp. Math. 346 (2004), 321--333.(with Y. Kamiya)
  39. $E(2)_*$-invertible spectra smashing with the Smith-Toda spectrum $V(1)$ at the prime 3 , Proc. Amer. Math. Soc. 132 (2004), 3111-3119. (with I. Ichigi)
  40. Homotopy groups of a generalized $E(2)$-local Moore spectrum at the prime three, Hiroshima Math. J. 35 (2005), 125--142. (with I. Ichigi)
  41. On the homotopy groups of $E(n)$-local spectra with unusual invariant ideals, Geometry & Topology Monographs 10 (2007) 319--332 (with H. Nakai)
  42. Picard groups of some local categories, Publ. RIMS, Kyoto Univ. 43-2 (2007), 303--314. (with Y. Kamiya)
  43. On subgroups of $\pi_*(L_2T(1)\wedge M(2))$ at the prime two, Bol. Soc. Mat. Mexicana. vol. 13-1, (2007), 207--230 (with I. Ichigi and X. Wang)
  44. The modulo two homotopy groups of the $L_2$-localization of the Ravenel spectrum, Cubo Math. J. 10-3 (2008), 43--55. (with I. Ichigi)
  45. 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, Vol.3-1(2010), 107-118. (with I. Ichigi)
  46. The homotopy groups of L_2-localization of the Ravenel spectra T(m)/v_1 at the prime two, Bulletin of the Mexican Mathematical Society, 16-1 (2010), 53-62.(with I. Ichigi and R. Takeda)
  47. Note on beta elements in homotopy, and an application to the prime three case, Proc. Amer. Math. Soc. 138 (2010), 1495-1499
  48. The beta elements $\be_{tp^2/r}$ in the homotopy of spheres, Algebraic and Geometric Topology 10 (2010) 2079-2090.
  49. On the chromatic $Ext^0(M^1_{n-1})$ on $\Gamma(m+1)$ for an odd prime, Hiroshima Math. J. 41 (2011), 211--222. (with R. Kitahama)
  50. The cohomology of $S(n,n-1)$ relevant to the Morava stabilizer algebra at an odd prime, Kochi Journal of Mathematics 7 (2012), 109-118. (with S. Tokashiki)
  51. Products of greek letter elements dug up from the third morava stabilizer algebra, Algebraic and Geometric Topology 12 (2012), 951-961. (with R. Kato)
  52. The first line of the Bockstein spectral sequence on a monochromatic spectrum at an odd prime, Nagoya Mathematical Journal 207 (2012), 139-157. (with R. Kato)
  53. A beta family in the homotopy of spheres, Proceedings of the American Mathematical Society 142 (2014), 2921--28.
  54. On the product $\alpha_1\beta_1^r\gamma_t$ in the stable homotopy groups of spheres, Kochi Journal of Mathematics 9 (2014), 169-172. (with K. Yoshizawa)
  55. Generalized Bousfield lattices and a generalized retract conjecture, Publ. RIMS. Kyoto Univ. 50-3(2014), pp. 497--513. (with R. Kato and Y. Tatehara)
  56. 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), 303-321. (with H. Okajima)
  57. A note on Hopkins' Picard groups of the stable homotopy categories of $L_{n}$-local spectra, Publ. RIMS. Kyoto Univ. 56-1(2020), 195-205
  58. Notes on an algebraic stable homotopy category, Bousfield classes and Ohkawa's theorem:Nagoya, Japan, August 28-30, 2015, Springer Proc. Math. Stat., 309, 2020, 103-108. (with R. Kato and H. Okajima)
  59. A note on products in stable homotopy groups of spheres via the classical Adams spectral sequence, Math. J. Okayama Univ. 63(2021), 107-122. (with R. Kato)
  60. 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), 177-203. (with I. Ichigi)
  61. 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), 6337-6361
  62. Beta families arising from a $v_2^9$ self map on $S/(3,v_1^8)$, Algebraic & Geometric Topology 23:9 (2023), 4349-4378 (with E. Belmont)
  63. On products of beta and gamma elements in the homotopy of the first Smith-Toda spectrum, to appear in Algebraic & Geometric Topology (with M. Shimomura)
  64. Generalized Moore spectra and Hopkins' Picard groups for a smaller chromatic level, ASETMJ 17(2) (2024), pp. 91-109. (with R. Kato, Y. Kawamoto, and H. Okajima)

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Papers (Kiyo et al)

  1. Note on invariant regular ideals in BP_* , J. Fac. Educ. Tottori Univ. (Nat. Sci.) 37 (1988), 103--110.
  2. Invariant regular sequences in the Brown-Peterson homology BP_* (with C. Takamura), J. Fac. Educ. Tottori Univ. (Nat. Sci.) 38 (1989), 67--75.
  3. Note on the right unit map and some elements of the Brown-Peterson homology, J. Fac. Educ. Tottori Univ. (Nat. Sci.) 38 (1989), 77--89.
  4. 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), 85--94.
  5. The chromatic E_1-term H^1M^1_2 and its application to the homology of the Toda-Smith spectrum V(1), J. Fac. Educ. Tottori Univ. (Nat. Sci.) 39 (1990), 63--83. Corrections to ``The chromatic E_1-term H^1M^1_2 and its application to the homology of the Toda-Smith spectrum V(1)'', J. Fac. Educ. Tottori Univ. (Nat. Sci.) 41 (1992), 7--11.
  6. The chromatic E_1-term H^0M^2_n for n> 1, J. Fac. Educ. Tottori Univ. (Nat. Sci.) 39 (1990), 103--121.
  7. On the 2nd obstruction on the existence of the Toda-Smith V(4), J. Fac. Educ. Tottori Univ. (Nat. Sci.) 40 (1991), 1--6.
  8. On the E_2-term of the Novikov spectral sequence for a Thom spectrum, J. Fac. Educ. Tottori Univ. (Nat. Sci.) 40 (1991), 25--32.
  9. Note on the Bousfield localization with respect to E(n), J. Fac. Educ. Tottori Univ. (Nat. Sci.) 41 (1992), 1--5.
  10. On differential of a generalized Adams spectral sequence, J. Fac. Educ. Tottori Univ. (Nat. Sci.) 41 (1992), 119--131.
  11. Homotopy groups of L_2-localized 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 , 9--34.
  12. A generalized Adams spectral sequence based on a BP -associated spectrum, J. Fac. Educ. Tottori Univ. (Nat. Sci.) 42 (1993), 1--15.
  13. 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), 17--30.
  14. The Ext groups H^0M_2^1(1) (with H. Mitsui), J. Fac. Educ. Tottori Univ. (Nat. Sci.) 42 (1993), 85--101.
  15. The homotopy groups of some L_n-local spectra (with R. Otsubo), J. Fac. Educ. Tottori Univ. (Nat. Sci.) 43 (1994), 1--6.
  16. A note on the chromatic convergence theorem, J. Fac. Educ. Tottori Univ. (Nat. Sci.) 43 (1994), 15--20.
  17. Chromatic E_1-terms --- up to April 1995, J. Fac. Educ. Tottori Univ. (Nat. Sci.) 44 (1995), 1--6.
  18. On a stable homotopy of a spectrum at the prime 3, J. Fac. Educ. Tottori Univ. (Nat. Sci.) 44 (1995), 7--11.
  19. Realization of a subalgebra of a generalized Steenrod algebra, J. Fac. Educ. Tottori Univ. (Nat. Sci.) 44 (1995), 103--110.
  20. A novice's guide to calculation of the Bockstein spectral sequences, J. Fac. Educ. Tottori Univ. (Nat. Sci.) 45 (1996), 1--24.
  21. 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), 25--34.
  22. Note on the $\beta$ family in the homotopy of spheres, J. Fac. Educ. Tottori Univ. (Nat. Sci.) 45 (1996), 103--110.
  23. The chromatic E_1-term 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), 63--71.

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Preprints

  1. The homotopy groups of $L_2V(1\frac 12)$ and an invertible spectrum at the prime three, preprint. (with I. Ichigi)
  2. The $\beta_{9t+3}$ in stable homotopy of spheres at the prime 3, preprint.
  3. Picard group of the $E(2)$-local stable homotopy category at the prime three, preprint.
  4. A beta family in the homotopy of spheres, preprint.

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