We introduce the notion of base change for a triangulated category over a base scheme following an article of Kuznetsov (https://arxiv.org/abs/0711.1734). We first embed a generic triangulated category as a component of a semiorthogonal decomposition of the derived category of a variety, then, when a base change is given, we show how to obtain a corresponding semiorthogonal decomposition of the derived category of the fiber product. If time allows, we show that the construction is independent on the embedding. The independence on the embedding is useful when we consider a triangulated category as an example of noncommutative algebraic variety. We will give a short introduction on derived categories with an emphasis on derived functors. The talk is 40 minutes long.

## Semiorthogonal Decompositions and Base Change

Research Group:

Warren Cattani

Institution:

SISSA

Location:

A-136

Schedule:

Thursday, December 5, 2019 - 16:00

Abstract: