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In mathematics, the Arason invariant is a cohomological invariant associated to a quadratic form of even rank and trivial discriminant and Clifford invariant over a field ''k'' of characteristic not 2, taking values in H3(''k'',Z/2Z). It was introduced by . The Rost invariant is a generalization of the Arason invariant to other algebraic groups. ==Definition== Suppose that ''W''(''k'') is the Witt ring of quadratic forms over a field ''k'' and ''I'' is the ideal of forms of even dimension. The Arason invariant is a group homomorphism from ''I''3 to the Galois cohomology group H3(''k'',Z/2Z). It is determined by the property that on the 8-dimensional diagonal form with entries 1, –''a'', –''b'', ''ab'', -''c'', ''ac'', ''bc'', -''abc'' (the 3-fold Pfister form«''a'',''b'',''c''») it is given by the cup product of the classes of ''a'', ''b'', ''c'' in H1(''k'',Z/2Z) = ''k'' */''k'' *2. The Arason invariant vanishes on ''I''4, and it follows from the Milnor conjecture proved by Voevodsky that it is an isomorphism from ''I''3/''I''4 to H3(''k'',Z/2Z). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Arason invariant」の詳細全文を読む スポンサード リンク
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