Index  I adic completion  absolute value  adically complete  archimedean  ramification index  decomposition  Dedekind domain  discrete  discretely valued  discrete valuation  discretely valued field  discrete valuation ring  Eisenstein  equal characteristic  global field  inertial subgroup  integral  integral closure  integrally closed  inverse limit  local field  localise  localisation  mixed characteristic  equivalent  non archimedean  norm  perfect  place  profinite topology  ramified  ramifies  ramified  ramification index  Teichm ller  Teichm ller lift  totally ramified  tame quotient  tamely ramified  uniformiser  unramified  valued field  valuation ring  valuation  wild inertial group  wildly ramified