Hypercovers, Sheafification, and Applications

In this talk we begin by reviewing the usual sheafification construction for presheaves of sets, and observe already how hypercovers come into play. We will try and highlight which properties are used from the structure of a Grothendieck topology along the way. Next, having set this familiar construction up in a way that generalizes to simplicial presheaves, we describe the "plus construction" as a colimit over all hypercovers and discuss what it would take to show that this results in a simplicial sheaf in the local projective model structure. Up until this point in the talk, the methods and sites considered are fairly general, and so should apply to many settings. Finally, we end by describing joint work with Micah Miller, Thomas Tradler, and Mahmoud Zeinalian in refining invariants for coherent sheaves and non-abelian gerbes using these constructions in more specialized settings. 

https://zoom.us/j/93172910947
Meeting ID: 931 7291 0947
For password please contact Christian Kaiser (kaiser@mpim-bonn.mpg.de).