All Questions

Let $A:= \underset{\lambda \in \Lambda}{\varinjlim} \,A_{\lambda}$ be an inductive limit of geometric regular local ring $(A_{\lambda}, {\frak m}_{\lambda})$, whose transition map $\phi_{\mu\lambda} \...

Let $f\in\mathbb{Z}_p[X]$ and let $Z_{f,p}(T)\in\mathbb{Z}_{(p)}(T)$ be the $p$-adic Igusa zeta polynomial (i.e. $Z_{f,p}(p^{-s})$ is the $p$-adic Igusa zeta function in the complex variable $s$, with ...

Let $X$, $Y$, $Z$ be integral schemes of finite type over a field $K$ (i.e., locally affine opens are finitely-generated algebras over $K$). Suppose we have the following condition$\colon$ $f \colon ...

For $A \colon= {\Bbb F}_p[[X_1,...,X_d]]$, by generalising Popescu-Neron's method, Spivakovski proved that $A$ is written by smooth sub-algebras. That is, $A \cong \underset{\lambda \in \Lambda}{\...