Rigid rational homotopy types. Issue 2 (22nd April 2014) - Lazda, Christopher
Abstract : In this paper, we define a rigid rational homotopy type associated to any varietyX over a perfect fieldk of positive characteristic. We prove comparison theorems with previous definitions in the smooth and proper, and log‐smooth and proper case. Using these, we can show that ifk is a finite field, then the Frobenius structure on the higher rational homotopy groups is mixed. We also define a relative rigid rational homotopy type, and use it to define a homotopy obstruction for the existence of sections