6 problems

Generalized henselianity conjecture. The ring $R$ is a henselian local ring.

Let $R$ be an excellent henselian discrete valuation ring with separably closed residue field $F$, and let $X$ be an object of the category of quasi-semistable pairs. Let…

Let $A$ be an almost commutative separated local ring. Denote by $\bar{A}$ the intersection of all local Henselian rings $H$ in the completion $\hat{A}$ such that…

Let $A$ be a Henselian local ring, let $\widehat A$ denote its completion, let $B$ be a finitely generated $A$-algebra, and let $\varphi:B\longrightarrow\widehat A$ be an $A$-morph…

Let $R$ be a ring for which a “smallest” Henselian extension can be defined, and let $\widehat{R}$ denote its completion. The algebraic closure of $R$ in $\widehat{R}$ consists of…

Artin's approximation conjecture. If $A$ is an excellent Henselian local ring, then $A$ has the Artin Approximation Property.