ABSTRACT
This chapter deals with glider representations defined over unbounded standard filtrations appearing in (non-commutative) geometry. Filtered localization techniques are developed, which are then used to develop a scheme theory for glider representations. With an eye towards non-commutative geometry we allow schemes over non-commutative rings with particular attention to so called almost commutative rings. We consider particular cases of R (e.g. for some P.I. ring Proj R) in terms of prime ideals, R-tors in terms of torsion theories and W(R) in terms of a non-commutative Grothendieck topology based on words of Ore set localizations.
