Homological stabilization for the orthogonal and symplectic groups

@article{Panin1990HomologicalSF,
  title={Homological stabilization for the orthogonal and symplectic groups},
  author={Ivan Alexandrovich Panin},
  journal={Journal of Soviet Mathematics},
  year={1990},
  volume={52},
  pages={3165-3170}
}
It is proved that for a commutative ring R with identity and without finite residue R, fields, the integral groups of homologies Hp(sp2n(R)) and Hp(O2n(R)) for a fixed p do not vary with the growth of n only if n⩾2p+dim X Here dim X is the Krull dim X-dimension of the spectrum of the maximal ideals of the ring R.