Algebra/Topology seminar

Speaker: Jack Davies

Title: Reconstruction and affineness in spectral algebraic geometry

Abstract: We will discuss a simplified proof and a generalisation of Mathew--Meier's famous affineness theorem in spectral algebraic geometry; in particular, this implies that quasi-coherent sheaves on the moduli stack of oriented elliptic curves (resp. its compactification) are equivalent to modules over TMF (resp. Tmf). This generalisation leads to a related concept which we call reconstruction, which identifies then mapping spaces between stacks are equivalent to mapping spaces between their global sections. At the end, we will mention some immediate consequences of these results to descent spectral sequences. This is joint work with William Balderrama and Sil Linskens.