Conditions under which $K₂(𝓞_F)$ is not generated by Dennis-Stein symbols

• Autorzy: Kevin Hutchinson
• Języki publikacji: EN

Kategorie tematyczne

• 19C20: Symbols, presentations and stability of K 2
• 19F15: Symbols and arithmetic

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 89
• Numer: 2
• Strony: 189-199

Daty

wydano

1999

otrzymano

1998-08-11

poprawiono

1998-10-19

Twórcy

autor

Kevin Hutchinson

• Mathematics Department, University College Dublin, Belfield, Dublin 4, Ireland

Bibliografia

• [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] 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] M. Geijsberts, On the generation of the tame kernel by Dennis-Stein symbols, J. Number Theory 50 (1995), 167-179.
• [4] J. Hurrelbrink, On K₂(𝓞) and presentations of $Sl_n(𝓞)$ in the real quadratic case, J. Reine Angew. Math. 319 (1980), 213-220.
• [5] J. Hurrelbrink, On the size of certain K-groups, Comm. Algebra 10 (1982), 1873-1889.
• [6] F. Keune, On the structure of the K₂ of the ring of integers of a number field, K-Theory 2 (1989), 625-645.
• [7] J. Milnor, Introduction to Algebraic K-Theory, Ann. of Math. Stud. 72, Princeton Univ. Press, 1971.
• [8] T. Mulders, Generating the tame and wild kernels by Dennis-Stein symbols, K-Theory 5 (1992), 449-470.
• [9] T. Mulders, On a map from K₀ to K₂, Ph.D. thesis, Katholiecke Universiteit Nijmegen, 1992.
• [10] J. Neukirch, Class Field Theory, Springer, Berlin, 1986.
• [11] A. A. Suslin, Torsion in K₂ of fields, K-Theory 1 (1987), 5-29.
• [12] J. Tate, Relations between K₂ and Galois cohomology, Invent. Math. 36 (1976), 257-274.
• [13] W. van der Kallen, Stability for K₂ of Dedekind rings of arithmetic type, in: Lecture Notes in Math. 854, Springer, 1981, 217-248.