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Milnor \(K\)-theory of local rings with finite residue fields. (English) Zbl 1190.14021

The Milnor \(K\)-theory of fields extends easily to a so called naive Milnor \(K\)-theory of local rings \((A,m,k)\), which is still a good cohomology theory if \(k\) is infinite. Here it is defined an improved Milnor \(K\)-theory in the case when \(k\) is finite. The main theorem says that the so called motivic cohomology ring \((H_{\mathrm{mot}}^n(\mathrm{Spec }(A),{\mathbb{Z}}(n)))_{n\geq 0}\) is generated by elements of degree one for a regular local equicharacteristic ring \(A\).

MSC:

14F42 Motivic cohomology; motivic homotopy theory
19D50 Computations of higher \(K\)-theory of rings
19E15 Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects)
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