|DATE||October 12 (Fri), 2018|
|TITLE||Proper base change for lcc \'etale sheaves of spaces I|
In this talk, I'll generalize the proper base change theorem in \'etale cohomology to space-valued sheaves, and provide two applications to the \'etale homotopy theory: the profinite \'etale homotopy type functor commutes with finite products and the symmetric powers of proper schemes over a separably closed field, respectively. In particular, the commutativity of the \'etale fundamental groups with finite products will be extended to all higher homotopy groups. In the applications, we'll see the advantage of the infinity categorical approach in \'etale homotopy theory over the model categorical one.