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Highest weight category structures on $Rep(B)$ and full exceptional collections on flag varieties over $\mathbb Z$
This paper constructs full exceptional collections in the bounded derived categories of coherent sheaves of flag schemes of Chevalley group schemes over $\mathbb Z$. The ensuing semiorthogonal decompositions are compatible with the Bruhat order on Weyl groups. The terms of full exceptional collections are a priori complexes of coherent sheaves; …