Jeroen Hekking (Universität Regensburg)

Derived blow-ups of classical schemes in quasi-smooth centers were first introduced by Kerz, Strunk and Tamme to solve Weibel’s conjecture on the vanishing of negative algebraic K-theory groups. This was generalized to quasi-smooth closed immersions of derived Artin stacks by Khan and Rydh, which has found applications in virtual intersection theory. In joint work with Khan–Rydh, this is further generalized to allow derived blow-ups in arbitrary centers. These were used in joint work with Rydh–Savvas to give a derived reduction of stabilizers algorithm.

The goal of this talk is to give an overview of some of the key ideas of this story which is accessible to geometers in general. We will pay particular attention to why derived algebraic geometry is useful, even if one is ultimately only interested in classical geometry.