Back to Algebraic Geometry Seminar: Fall 2020
Algebraic Geometry Seminar
Date: Tuesday, Sep 22, 2020
Time: 3:30PM - 4:30PM
Location: Zoom
Alicia Lamarche
University of Utah
Title |
Derived Categories, Arithmetic, and Rationality |
Abstract |
When trying to apply the machinery of derived categories in an arithmetic setting, a natural question is the following: for a smooth projective variety $X$, to what extent can $D^b(X)$ be used as an invariant to answer rationality questions? In particular, what properties of $D^b(X)$ are implied by $X$ being rational, stably rational, or having a rational point? On the other hand, is there a property of $D^b(X)$ that implies that $X$ is rational, stably rational, or has a rational point? In this talk, we will examine a family of arithmetic toric varieties for which a member is rational if and only if its bounded derived category of coherent sheaves admits a full etale exceptional collection. Additionally, we will discuss the behavior of the derived category under twisting by a torsor, which is joint work with Mattew Ballard, Alexander Duncan, and Patrick McFaddin. |
Algebraic Geometry