Stiefel Whitney classes for quadratic modules. (English) Zbl 0767.19004
Summary: Let \(A\) be a commutative ring with \(1/2\in A\). In the spirit of A. Grothendieck [Bull. Soc. Math. Fr. 86, 137-154 (1958; Zbl 0091.332)] by means of a quadratic flag bundle, we obtain Stiefel-Whitney classes
\[
\overline{SW}_ j:L^{ct}_ 0(A)\to\check H^ 0_{\text{Zar}}(\text{Spec} A,\;k_ j(\cdot))\quad (j\geq 0)
\]
for the Witt-Grothendieck group of quadratic modules of constant rank, with values in the group of global sections of the sheaf associated with \(k_ j=K_ j/2K_ j\), the Milnor \(K_ j\)-group mod 2.
MSC:
| 19G05 | Stability for quadratic modules |
| 19D45 | Higher symbols, Milnor \(K\)-theory |
| 19G12 | Witt groups of rings |
| 11E81 | Algebraic theory of quadratic forms; Witt groups and rings |
Keywords:
Milnor \(K_ j\)-group; quadratic flag bundle; Stiefel-Whitney classes; Witt-Grothendieck group of quadratic modules of constant rankCitations:
Zbl 0091.332References:
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