Recent zbMATH articles in MSC 19https://zbmath.org/atom/cc/192021-01-08T12:24:00+00:00WerkzeugOn the structures of \({K_2} (\mathbb{Z}[{C_6}])\) and \({K_2} (\mathbb{Z}[{C_{10}}])\).https://zbmath.org/1449.190012021-01-08T12:24:00+00:00"Zhang, Yakun"https://zbmath.org/authors/?q=ai:zhang.yakun"Tang, Guoping"https://zbmath.org/authors/?q=ai:tang.guopingSummary: Let \({C_n}\) be a cyclic group of order \(n\). We obtain the explicit structures of \({K_2} (\mathbb{Z}[{C_6}])\) and \(W{h_2} ({C_6})\), and the 2-primary torsion subgroup of \({K_2} (\mathbb{Z}[{C_{10}}])\) and \(W{h_2} ({C_{10}})\). Besides, we give the explicit structures of \({K_2} (\mathbb{Z}[{\zeta_3}][{C_2}])\) and the 2-primary torsion subgroup of \({K_2} (\mathbb{Z}[{\zeta_5}][{C_2}])\).Higher algebraic \(K\)-theory and representations of algebraic groups.https://zbmath.org/1449.190022021-01-08T12:24:00+00:00"Kuku, Aderemi"https://zbmath.org/authors/?q=ai:kuku.aderemi-oSummary: This paper is concerned with Higher Algebraic \(K\)-theory and actions of algebraic groups \(G\) on such `nice' categories as the category of algebraic vector bundles on a scheme \(X\). Such `nice' categories are examples of `exact' categories with the observation that the category of actions on \(G\) on such exact categories also form an exact category called equivariant exact categories on which one can do higher Algebraic \(K\)-theory (of Quillen) called equivariant higher Algebraic \(K\)-theory -- the higher dimensional generalizations of classical equivariant \(K\)-theory which belongs to the field of representation theory. Thus, for an Algebraic group \(G\) over a number field or \(p\)-adic field \(F\), we present constructions and computations of equivariant higher \(K\)-groups as well as `profinite' or `continuous' higher \(K\)-groups for some \(G\)-Scheme \(X\). In particular, we present explicit l-completeness (l a rational prime) and finiteness computations for higher \(K\)-groups and profinite higher \(K\)-groups for twisted flag varieties.