Skip to main content
MathOverflow

Return to Question

deleted 30 characters in body
Source Link
user158636
user158636

Let $X$ be a proper geometrically integral locally complete intersection $\mathbb{F}_p$-scheme.

Assume that $X$ is the special fiber of a proper flat $\mathbb{Z}_p$-scheme with a smooth generic fiber and that for each point $x\in X$ we have $\dim_{\kappa (x)}(\Omega _{X/\mathbb{F}_p, x}\otimes_{\mathcal{O}_{X, x}} \kappa (x))\leq 1+\dim(X)$.

Is $X$ the special fiber of a regular proper flat $\mathbb{Z}_p$-scheme?

Let $X$ be a proper geometrically integral locally complete intersection $\mathbb{F}_p$-scheme.

Assume that $X$ is the special fiber of a proper flat $\mathbb{Z}_p$-scheme with a smooth generic fiber and that for each point $x\in X$ we have $\dim_{\kappa (x)}(\Omega _{X/\mathbb{F}_p, x}\otimes_{\mathcal{O}_{X, x}} \kappa (x))\leq 1+\dim(X)$.

Is $X$ the special fiber of a regular proper flat $\mathbb{Z}_p$-scheme?

Let $X$ be a proper geometrically integral $\mathbb{F}_p$-scheme.

Assume that $X$ is the special fiber of a proper flat $\mathbb{Z}_p$-scheme with a smooth generic fiber and that for each point $x\in X$ we have $\dim_{\kappa (x)}(\Omega _{X/\mathbb{F}_p, x}\otimes_{\mathcal{O}_{X, x}} \kappa (x))\leq 1+\dim(X)$.

Is $X$ the special fiber of a regular proper flat $\mathbb{Z}_p$-scheme?

added 184 characters in body
Source Link
user158636
user158636

Let $X$ be a proper geometrically integral locally complete intersection $\mathbb{F}_p$-scheme. 

Assume that $X$ is the special fiber of a proper flat $\mathbb{Z}_p$-scheme with a smooth generic fiber and that for each point $x\in X$ we have $\dim_{\kappa (x)}(\Omega _{X/\mathbb{F}_p, x}\otimes_{\mathcal{O}_{X, x}} \kappa (x))\leq 1+\dim(X)$. 

Is $X$ the special fiber of a regular proper flat $\mathbb{Z}_p$-scheme?

Let $X$ be a proper geometrically integral $\mathbb{F}_p$-scheme. Assume $X$ is the special fiber of a proper flat $\mathbb{Z}_p$-scheme with a smooth generic fiber. Is $X$ the special fiber of a regular proper flat $\mathbb{Z}_p$-scheme?

Let $X$ be a proper geometrically integral locally complete intersection $\mathbb{F}_p$-scheme. 

Assume that $X$ is the special fiber of a proper flat $\mathbb{Z}_p$-scheme with a smooth generic fiber and that for each point $x\in X$ we have $\dim_{\kappa (x)}(\Omega _{X/\mathbb{F}_p, x}\otimes_{\mathcal{O}_{X, x}} \kappa (x))\leq 1+\dim(X)$. 

Is $X$ the special fiber of a regular proper flat $\mathbb{Z}_p$-scheme?

Source Link
user158636
user158636

Smoothable $\mathbb{F}_p$-variety embeds in a regular scheme

Let $X$ be a proper geometrically integral $\mathbb{F}_p$-scheme. Assume $X$ is the special fiber of a proper flat $\mathbb{Z}_p$-scheme with a smooth generic fiber. Is $X$ the special fiber of a regular proper flat $\mathbb{Z}_p$-scheme?