Characteristic Cycles and Representation Theory

该项目将经典代数几何与代数分析和拓扑方法相结合。它的主要目的是利用逆束理论和d模来研究阿贝尔变体的子变体。在这种情况下，中心作用是由共切束上的特征循环起作用，它捕获了关于奇点和分支的微妙信息。他们将高斯映射与线性代数群的表示联系起来，这些表示来自坦纳基形式主义。两种观点的结合可能会在代数几何中找到应用，并提高我们对正在产生的坦纳基群的理解。

The project combines classical algebraic geometry with methods from algebraic analysis and topology. Its main goal is to study subvarieties of abelian varieties via the theory of perverse sheaves and D-modules.In this context a central role is played by characteristic cycles on the cotangent bundle, which capture subtle information on singularities and ramification. They relate Gauss maps to the representations of linear algebraic groups arising from the Tannakian formalism. The combination of both viewpoints is likely to find applications in algebraic geometry and improve our understanding of the arising Tannakian groups.