Conditions under which K ( F ) is not generated by Dennis-Stein symbols

Kevin Hutchinson

Acta Arithmetica (1999)

  • Volume: 89, Issue: 2, page 189-199
  • ISSN: 0065-1036

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Kevin Hutchinson. "Conditions under which $K₂(_F)$ is not generated by Dennis-Stein symbols." Acta Arithmetica 89.2 (1999): 189-199. <http://eudml.org/doc/207263>.

@article{KevinHutchinson1999,
author = {Kevin Hutchinson},
journal = {Acta Arithmetica},
keywords = {Steinberg group; Steinberg symbol; Dennis-Stein symbol; biquadratic field},
language = {eng},
number = {2},
pages = {189-199},
title = {Conditions under which $K₂(_F)$ is not generated by Dennis-Stein symbols},
url = {http://eudml.org/doc/207263},
volume = {89},
year = {1999},
}

TY - JOUR
AU - Kevin Hutchinson
TI - Conditions under which $K₂(_F)$ is not generated by Dennis-Stein symbols
JO - Acta Arithmetica
PY - 1999
VL - 89
IS - 2
SP - 189
EP - 199
LA - eng
KW - Steinberg group; Steinberg symbol; Dennis-Stein symbol; biquadratic field
UR - http://eudml.org/doc/207263
ER -

References

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  1. [1] R. K. Dennis and M. R. Stein, The functor K₂: a survey of computations and problems, in: Lecture Notes in Math. 342, Springer, 1973, 243-280. 
  2. [2] R. K. Dennis and M. R. Stein, K₂ of radical ideals and semi-local rings revisited, in: Lecture Notes in Math. 342, Springer, 1973, 281-303. 
  3. [3] M. Geijsberts, On the generation of the tame kernel by Dennis-Stein symbols, J. Number Theory 50 (1995), 167-179. Zbl0822.11080
  4. [4] J. Hurrelbrink, On K₂() and presentations of S l n ( ) in the real quadratic case, J. Reine Angew. Math. 319 (1980), 213-220. Zbl0431.20038
  5. [5] J. Hurrelbrink, On the size of certain K-groups, Comm. Algebra 10 (1982), 1873-1889. Zbl0502.12010
  6. [6] F. Keune, On the structure of the K₂ of the ring of integers of a number field, K-Theory 2 (1989), 625-645. Zbl0705.19007
  7. [7] J. Milnor, Introduction to Algebraic K-Theory, Ann. of Math. Stud. 72, Princeton Univ. Press, 1971. Zbl0237.18005
  8. [8] T. Mulders, Generating the tame and wild kernels by Dennis-Stein symbols, K-Theory 5 (1992), 449-470. Zbl0761.11040
  9. [9] T. Mulders, On a map from K₀ to K₂, Ph.D. thesis, Katholiecke Universiteit Nijmegen, 1992. 
  10. [10] J. Neukirch, Class Field Theory, Springer, Berlin, 1986. Zbl0587.12001
  11. [11] A. A. Suslin, Torsion in K₂ of fields, K-Theory 1 (1987), 5-29. Zbl0635.12015
  12. [12] J. Tate, Relations between K₂ and Galois cohomology, Invent. Math. 36 (1976), 257-274. Zbl0359.12011
  13. [13] W. van der Kallen, Stability for K₂ of Dedekind rings of arithmetic type, in: Lecture Notes in Math. 854, Springer, 1981, 217-248. 

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