# Derived Algebraic Geometry Seminar — Fall 2017

## Organization

Organization
Johan Commelin and Salvatore Floccari
Location
Israëlslaan 118, Kelder 1.02. (Exceptions: see below)
Time
1400–1545, Friday. (Exceptions: see below)

Please note that there is a sibling seminar on Friday mornings: the Stacks seminar.

## Description

The goal of the seminar is to learn the basics of derived algebraic geometry with the purpose of understanding Huybrechts's proof of the following theorem.
Theorem. Let $S$ and $S'$ be two projective complex K3 surfaces and let $\phi\colon H^2(S,\mathbb{Q}) \to H^2(S',\mathbb{Q})$ be an Hodge isometry between them. Then $\phi$ yields an algebraic class in $H^{2,2}(S\times S',\mathbb{Q})$. In other words, $\phi$ is induced by an algebraic correspondence between $S$ and $S'$.
This result was first proven via analytic methods by Buskin. (Lenny Taelman organised an Intercity Seminar on his proof in the spring of 2016.) In contrast, Huybrechts's proof uses the language of derived algebraic geometry and Fourier–Mukai transforms in particular. During the course of the seminar, we will learn these techniques, and finally we discuss the proof of the aforementioned theorem. Our main reference is Huybrechts's book Fourier–Mukai transforms in algebraic geometry, and his preprint Motives of isogenous K3 surfaces.

## Schedule and location

A tentative schedule of talks can be found here.
DateTalk
Fri, Oct 06
(1100–1245)
Salvatore Floccari — Triangulated categories and the derived category of coherent sheaves.
Fri, Oct 13
Johan Commelin — A theorem of Bondal and Orlov. [Notes]
Fri, Oct 20
Salvatore Floccari — Fourier Mukai tranforms and Orlov's theorem.
Fri, Oct 27
Salvatore Floccari — Fourier Mukai tranforms and Orlov's theorem (continued).
Ties Laarakker — Fourier Mukai tranforms and abelian varieties.
Fri, Nov 10
(Duistermaatzaal,
5th floor, HFG)
Ties Laarakker — Fourier Mukai tranforms and abelian varieties (continued).
Fri, Nov 24
(Springerzaal,
7th floor, HFG)
Johan Commelin — Twisted sheaves. [Notes]
Fri, Dec 08
(Springerzaal,
7th floor, HFG)
Wessel Bindt — Twisted Fourier-Mukai functors and twisted Chern characters.

## Literature

The main source is the aforementioned book by Huybrechts, Fourier–Mukai transforms in algebraic geometry.