-
Henselization of A is
unique up to
unique isomorphism. The
Henselization of A is an
algebraic substitute for the
completion of A. The
Henselization of...
- {\displaystyle \kappa } . In this case, the
residue fields of the
Henselization and
strict Henselization differ ( R , p ) h ⇝ κ ( R , p ) s h ⇝ κ s e p {\displaystyle...
- an
excellent discrete valuation ring, let A {\displaystyle A} be the
henselization at a
prime ideal of an R {\displaystyle R} -algebra of
finite type,...
- {\displaystyle X\to S} over the
spectrum S {\displaystyle S} of the
henselization of k [ T ] {\displaystyle k[T]} , k {\displaystyle k} an algebraically...
- the
local ring at x for the étale
topology turns out to be the
strict henselization of the
local ring O X , x {\displaystyle {\mathcal {O}}_{X,x}} .[citation...
-
those series satisfying a
nontrivial polynomial equation),
which is the
henselization of the ring of
germs of
rational functions. In particular, it is a regular...
- of
proper convex subgroups of its
valuation group.
Hensel Henselian Henselization Named for Kurt
Hensel 1. Hensel's
lemma states that if R is a complete...
- such that Ah is
Henselian with
respect to mAh. This Ah is
called the
Henselization of A. If A is noetherian, Ah will also be noetherian, and Ah is manifestly...
- {\displaystyle x\in F(X)} is
called an
algebraic element if it is the
henselization of an O S {\displaystyle {\mathcal {O}}_{S}} -algebra of
finite type...
- ones. The
local contribution Hr(Kv, F) is the
Galois cohomology of the
Henselization Kv of K at the
place v,
modified a la Tate: H r ( K v , F ) = H T r...
