扭曲旗簇族的半正交分解
Semiorthogonal decompositions for families of twisted flag varieties
AI总结：
该研究将Samokhin-van der Kallen的半正交分解推广至拟分裂半单群，证明光滑扭曲广义旗簇族的导出范畴可半正交分解，实现了Panin关于扭曲旗簇Quillen K-理论计算的范畴化。
AI中文摘要：
我们证明光滑扭曲广义旗簇族的导出范畴，可分解为基上扭曲层的导出范畴的半正交分解。特别地，我们得到Panin关于扭曲旗簇的Quillen K-理论计算的范畴化。主要内容是将Samokhin-van der Kallen的半正交分解，从分裂单连通半单群的抛物子群表示范畴，推广到任意拟分裂半单群，包括非单连通情形。
英文摘要：
We show that the derived categories of smooth families of twisted generalized flag varieties admit semiorthogonal decompositions into derived categories of twisted sheaves over the base. In particular, we obtain a categorification of Panin's computation of the Quillen K-theory of twisted flag varieties. The main ingredient is a generalization of the Samokhin-van der Kallen semiorthogonal decomposition for representation categories of parabolic subgroups from split simply connected semisimple groups to arbitrary quasi-split semisimple groups, including non-simply connected cases.
