2
votes
0answers
52 views

lift isomorphic in a sufficiently thick fiber

Let $P$ and $P'$ two polynomials in $k[[\pi]][t]$ for an algebraically closed field $k$ and let $A=k[[\pi]]$. We consider $ X'=Spec (A[t]/(P'))$ and $X=Spec (A[t]/(P)$. Let $d=val(\Delta(P))$ where ...
13
votes
4answers
2k views

Is there a Galois correspondence for ring extensions?

Given an ring extension of a (commutative with unit) ring, Is it possible to give a "good" notion of "degree of the extension"?. By "good", I am thinking in a degree which allow us, for instance, to ...
2
votes
0answers
437 views

Decomposition group vs Galois group of completed extension for height > 1 primes

Assume Let $R$ be a Noetherian normal excellent domain, $F$ its field of fractions. Let $S$ be a finite $R$-algebra, $L$ its field of fractions. $L/F$ a (finite) Galois extension $S$ normal in $L$ ...