Derived categories, quasi-hereditary algebras, and toric geometry (A08)

派生范畴及其变换在几何、代数和表示理论中起着中心作用。在这个项目中，我们重点研究了在颤表示的射影代数变数和模空间上的可倾束的存在性和构造。有时衍生的等价关系涉及额外的信息，如t结构、对偶性、例外序列、正交分解或某些子类别。在许多情况下，最高权范畴和准遗传代数出现。

Derived categories and their transformations play a central role in geometry, algebra and representation theory. In this project we focus on the existence and construction of tilting bundles on projective algebraic varieties and moduli spaces of quiver representations. Sometimes derived equivalences respect additional information like t-structures, dualities, exceptional sequences, orthogonal decompositions or certain subcategories. In many cases highest weight categories and quasi-hereditary algebras show up.