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 quasicoherent sheaves on the moduli 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” quasicoherent
sheaves on this stack. This acts as a 1-parameter deformation of
quasicoherent 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.