Student AG Seminar: Derived Category of GIT Quotient

Arkamouli Debnath, UW
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PDL C-401

Geometric Invariant Theory (GIT) is the theory of defining quotients in Algebraic Geometry. In his paper https://arxiv.org/abs/1203.0276 (The Derived Category of a GIT quotient) Halpern-Leistner sets up a way of thinking about the derived category of a GIT quotient and in particular gives a semiorthogonal decomposition of the derived category of $[X/G]$ where one of the components is the derived category of $[X^{ss}/G]$ where $G$ is a reductive group, $X$ is a variety and $X^{ss}$ is the GIT semistable locus. In this talk I will start with a short introduction to GIT and try to give a roadmap to how we get such a semiorthogonal decomposition. It will involve the idea of what are called "window categories" which are extremely important tools being used in this area recently.

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