# Jeroen Hekking: Graded algebras, projective spectra and blow-ups in derived algebraic geometry

**Time: **
Thu 2021-11-25 15.30 - 16.30

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan (alt. Zoom, meeting ID: 921 756 1880)

**Lecturer: **
Jeroen Hekking (KTH Royal Institute of Technology)

**Abstract:** The goal of this talk is to define the derived blow-up of a closed immersion of derived schemes, and to mention a few key properties of this construction. After reviewing derived schemes, we will first introduce the infinity category of graded, simplicial rings as a free completion along sifted colimits, and explain how one takes the derived projective spectrum of such a gadget. We then introduce the derived extended Rees algebra via Weil restrictions, which is the key ingredient for derived blow-ups.