Vorträge des SFB 1442

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.

Given a finitely generated group G, a non-trivial element g\in G, and a minimal action of G on a compact space X, with amenable neighborhood stabilizers, we prove sufficient conditions in terms of various growth/decay functions for topological freeness of the action of g on X. We apply our results to the case of the (Furstenberg) boundary action of G, to conclude C*-simplicity under (sub)rapid decay conditions. In this context, we also give a description of the support of stationary states on the reduced C*-algebra of G. This is joint work with Nazmul Alam, Joseph Gondek, and Randy Pham.