The weight-two motivic complex of equicharacteristic local fields. (Q1398209)

Let \(L/K\) be a finite Galois extension of local fields in positive characteristic with Galois group \(G\). The weight-two motivic complex \(\Gamma(2,L)\) defines an element of \(\text{Ext}^2_{\mathbb{Z}[G]}(K_2(L),K_3(L))\). The author shows, after inverting the prime 2, that the cup-product with this 2-extension induces an isomorphism on Tate cohomology of \(G\). In fact, he shows that this isomorphism coincides with the cup product by \(K_2/K_3\) local fundamental class previously constructed by himself.