The Karoubi tower and \(K\)-theory invariants of Hermitian forms
The object of this paper is to generalise certain quadratic form invariants (the rank, the discriminant, the total Hasse-Witt invariant and the Clifford invariant). The new invariants are defined for any Hermitian ring \(R\), and they form an infinite sequence \(\phi_0,\phi_1,\phi_2,\ldots\;\). The method is based on the Karoubi tower constructed by \textit{D. Kobal} in ``\(K\)-theory, Hermitian \(K\)-theory and the Karoubi tower'' [\(K\)-Theory 17, No. 2, 113-140 (1999; Zbl 0931.19003) - see the review above]. From the Karoubi tower one gets a group \(W\) generalising the Witt ring and a filtration \[ \ldots \subset I_2 \subset I_1 \subset I_0=W. \] The invariant \(\phi_n\) is the quotient homomorphism \(I_n\to I_n/I_{n+1}\); the image \(I_n/I_{n+1}\) can be expressed in terms of the algebraic \(K\)-theory group \(K_n R\).
scientific article; zbMATH DE number 1332923