Algebra/Topology Seminar

Speaker: Marius Nielsen

Title: On the geometrization of synthetic spectra

Abstract: The category of synthetic spectra is a strong tool for understanding the Adams-Novikov spectral sequence and acts as a 1-parameter deformation between spectra and quasi-coherent sheaves on the moduli stack of formal groups. One perspective on the Adams-Novikov spectral sequence is that it is the descent spectral sequence for the moduli stack of formal groups. In this talk I will present an approach which, to any geometric (non-connective) spectral stack X, produces a category of “synthetic” quasi-coherent sheaves on this stack. This acts as a 1-parameter deformation of quasi-coherent sheaves and provides a natural place to study the descent spectral sequence of X. If time permits, I will discuss the relationship with synthetic spectra and the even stack of Hahn—Raksit—Wilson.