A homotopy exact sequence and unipotent fundamental groups over function fields

12 June 2014
Christopher Lazda
If X/F is a smooth and proper variety over a global function field of characteristic p, then for all l different from p the co-ordinate ring of the l-adic unipotent fundamental group is a Galois representation, which is unramified at all places of good reduction. In this talk, I will ask the question of what the correct p-adic analogue of this is, by spreading out over a smooth model for C and proving a version of the homotopy exact sequence associated to a fibration. There is also a version for path torsors, which enables me to define an function field analogue of the global period map used by Minhyong Kim to study rational points.
  • Number Theory Seminar