SMF

Improved stability for SK1 and WMSd of a non-singular affine algebra

Improved stability for SK1 and WMSd of a non-singular affine algebra

Ravi RAO, Wilberd VAN DER KALLEN
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  • Année : 1994
  • Tome : 226
  • Format : Électronique
  • Langue de l'ouvrage :
    Anglais
  • Pages : 411-420
  • DOI : 10.24033/ast.284

We establish some stability results for K1 of algebras over algebraically closed fields, whose analogues fail for algebras over the reals. More technically, let k be a perfect C1 field and A a non-singular affine algebra of Krull dimension d3 over k. Then we show SLr(A)/Er(A)SK1(A) is an isomorphism for rd+1 and we find a homomorphism SLd(A)WMSd(A) whose kernel is SLd1(A)Ed(A), which is thus shown to be a normal subgroup.



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