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DAG III: examples

Introductory Workshop: Derived Algebraic Geometry and Birational Geometry and Moduli Spaces January 31, 2019 - February 08, 2019

February 04, 2019 (11:30 AM PST - 12:30 PM PST)
Speaker(s): Benjamin Antieau (University of Illinois, Chicago)
Location: MSRI: Simons Auditorium



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 Toën--Vaquié 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 Fourier--Mukai equivalences.

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H.264 Video 862_25975_7591_10-Antieau.mp4
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