姜清元,Universigy of Edinburgh

The framework of derived algebraic geometry (DAG), developed by Toen-Vezzosi, Lurie and many others, allows us to extend Grothendieck’s theory of flag schemes of sheaves to the cases of complexes. In the first half of the talk, we will define and study flag schemes of complexes using DAG.

The Borel–Weil–Bott theorem provides a fundamental link between algebraic geometry and representation theory. In the second half of the talk, we will establish a derived generalization of the Borel—Wei—Bott theorem for flag schemes of [-1,0]-perfect complexes.

Based on the second part of the paper arXiv:2212.10488.