The Stacks project

Try to use L/K notation for field extensions

We could also try to consistenly use "field extension" and not just
"extension" and consistently use "ring extension", etc.

More ramification theory

To me this is almost as bad as henselization; probably means that
there is a lot of room for improvement in the writing of this
material.

Neurotic changes

Given a finite extension L/K of the fraction field of a discrete
valuation ring, we say L/K is 'unramified wrt A' instead of just saying
that it is 'unramified'. There are two reasons:

  1. There may be more than one dvr whose fraction field is K
  2. We already have a notion of an unramified ring map and we do not
  want the reader to think we are asking K ---> L to be unramified as a
  ring map...

Yes, this is probably not necessary...

Tags: Added new tags

Standard material about Galois extensions of ff of dvrs