Grothendieck-Witt groups of quadrics
  Let k be a commutative ring containing 1/2. In this paper, we construct certain homotopy fibration sequences for Grothendieck-Witt spectra of smooth quadric hypersurfaces over k. As an application, we compute Witt groups of smooth quadric hypersurfaces over certain kinds of bases. 
Heng XIe
math.KT