Jan 31, 2019
Thursday

09:30 AM  10:30 AM


DAG I: the cotangent complex and derived de Rham cohomology
Benjamin Antieau (University of Illinois, Chicago)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
In this series of lectures, I will give an introduction to derived algebraic geometry aimed at algebraic geometers. The first lecture will introduce simplicial commutative rings and use them to define the cotangent complex and derived de Rham cohomology with several examples. The second lecture will introduce derived stacks and the moduli stack of objects in a derived category. Then, I will give the geometricity theorem of ToënVaquié and describe the cotangent complex to the moduli stack. In the third lecture, we will use the machinery developed in the first two lectures to study three examples: cohomology as maps to a geometric derived stack, the (derived) Picard stack, and the stack of FourierMukai equivalences.
 Supplements

Notes
713 KB application/pdf



Feb 01, 2019
Friday

11:00 AM  12:00 PM


DAG II: moduli of objects in derived categories
Benjamin Antieau (University of Illinois, Chicago)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
In this series of lectures, I will give an introduction to derived algebraic geometry aimed at algebraic geometers. The first lecture will introduce simplicial commutative rings and use them to define the cotangent complex and derived de Rham cohomology with several examples. The second lecture will introduce derived stacks and the moduli stack of objects in a derived category. Then, I will give the geometricity theorem of ToënVaquié and describe the cotangent complex to the moduli stack. In the third lecture, we will use the machinery developed in the first two lectures to study three examples: cohomology as maps to a geometric derived stack, the (derived) Picard stack, and the stack of FourierMukai equivalences
 Supplements

Notes
639 KB application/pdf



Feb 04, 2019
Monday

11:30 AM  12:30 PM


DAG III: examples
Benjamin Antieau (University of Illinois, Chicago)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
In this series of lectures, I will give an introduction to derived algebraic geometry aimed at algebraic geometers. The first lecture will introduce simplicial commutative rings and use them to define the cotangent complex and derived de Rham cohomology with several examples. The second lecture will introduce derived stacks and the moduli stack of objects in a derived category. Then, I will give the geometricity theorem of ToënVaquié and describe the cotangent complex to the moduli stack. In the third lecture, we will use the machinery developed in the first two lectures to study three examples: cohomology as maps to a geometric derived stack, the (derived) Picard stack, and the stack of FourierMukai equivalences.
 Supplements

Notes
650 KB application/pdf


