Filtrations and Buildings

We construct and study a scheme theoretical version of the Tits vectorial building, relate it to ltrations on ber functors, and use them to clarify various constructions pertaining to ane Bruhat-Tits buildings, for which we also provide a Tannakian description. ContentsChapter 1.The decomposition of C Γ (G) is compatible with the partially ordered (weak=strong) monoid structures: for x = (x r , x c ) and y = (y r , yx + y = (x r + y r , x c + y c ) and x ≤ y ⇐⇒ (x r ≤ y r and x c = y c ) .This is easily checked by reduction to the split case, cf.section 2.4.10 below. Relative positions of Γ-ltrationsLet G be a reductive group over S. 5.7.