Homological stabilization for the symplectic and orthogonal groups

I. A. Panin

Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 8, Tome 160 (1987), pp. 222-228

Résumé

It is proved that for a commutative ring $R$ with identity and without finite residue $R$, fields, the integral groups of homologies $Hp(sp_{2n}(R))$ and $Hp(O_{2n}(R))$ for a fixed $p$ do not vary with the growth of $n$ only if $n\geq2p+\dim X$. Here $\dim X$ is the Krull $\dim X$-dimension of the spectrum of the maximal ideals of the ring $R$.