Research proof index

The local ramification index for the extension L_w/K_v is equal to the global ramification index for the extension w/v. In other words, if x in K_v and i:K_v->L_w then w(i(x))=v(x)^e where e is computed globally.

If w | v then for a ∈ A we have w(a)=v(a)^e where e is the ramification index.

The image of B ⊗[A] 𝓞_v (the closure of B) in ∏_w L_w is closed.

The image of B ⊗[A] 𝓞_v in ∏_w L_w is ∏_w 𝓞_w.

The image of B ⊗[A] 𝓞_v in L ⊗[K] K_v is the closure of the image of B.

The image of B ⊗[A] 𝓞_v in L ⊗[K] K_v is clopen.