Galois Deformation Theory for Norm Fields and its Arithmetic Applications.
Wansu Kim · Deep Blue (University of Michigan) · 2009
Let K be a finite extension of Q_p, and choose a uniformizer pi in K. Choose pi_{n+1} such that pi_1:=pi and pi_{n+1}^p=pi_n, and let K_infty denote the field extension of K obtained by adjoining pi_{n+1} for all n. We introduce a new technique using restriction to Gal(Kbar/K_infty) to study deformations and mod p reductions in p-adic Hodge theory. One of our main results in deformation theory is the existence of deformation rings for Gal(Kbar/K_infty)-representations "of height 0. We also obtain equi-characteristic deformation rings for Galois representations that come from local shtukas, and study their local structure.