Cohomological intersection theory and derived algebraic geometry

Time and place

Room 617, 6F, Astro Math. Building (NTU Campus)
Jan. 12 (Wed), 19 (Wed), and 24 (Mon), 10:00 – 12:00
If you would like to attend online, send me an email.

Description

In these lectures, we will explain a cohomological approach to intersection theory on schemes and stacks. By working with Voevodsky's theory of motivic cohomology, we will see that this recovers and extends the cycle-theoretic approach of Fulton (and its extension to stacks by Kresch). Moreover, we will use the language of derived algebraic geometry to systematically incorporate non-transversality phenomena, most notably Kontsevich's virtual fundamental classes. We will discuss examples related to curve counting, cohomological Hall algebras, and even Shimura varieties, depending on participants' interests. No prior knowledge of stacks or derived geometry will be assumed.

Lecture notes

Notes as of Jan. 16