Local fundamental classes derived from higher \(K\)-groups. III (Q2704209)

This is the third paper of a series by the author [see Proc. Great Lakes \(K\)-theory Conf., Fields Inst. Commun. 16, 285-323 (1997; Zbl 0885.11064) and 325-344 (1997; Zbl 0889.11042)] on the construction of local fundamental classes derived from algebraic \(K\)-groups in dimensions \(2r\), \(2r+1\), for any \(r\geq 0\). Here he studies, in positive characteristic, the connection between the \(K_2/K_3\) fundamental class and Lichtenbaum's motivic complex of weight two. For a Galois extension \(L/K\) of local fields of positive characteristic, the \(K_{2r}/K_{2r+1}\) fundamental class has an associated Euler characteristic \(\Omega_r(L/K,2)\) which lives in the class group \(\text{Cl}(\mathbb{Z} [G(L/K)])\). The main role of these local invariants is to construct the higher \(K\)-theoretical analogues of the second Chinburg invariant, \(\Omega_r(E/F,2)\), of a Galois extension of global fields of positive characteristic. The author explains how to calculate \(\Omega_1(E/F,2)\) in the tame case.NEWLINENEWLINEFor the entire collection see [Zbl 0956.00036].