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Hi,

I would like to understand and prove the following two "well-known" facts:

1)

If $B$ is a scheme and $P$ a property for which I know:

i) if $B=Spec(V)$ where $V$ is a complete DVR, thenif $P$ holdsholds on an open subsetthe special point then it holds on the generic point of $B$

ii) $P$ is true on a constructible set of $B$

then $P$ holds on an open subset of $B$.

2)

Assume $B$ integral. If $P$ true on the generic fiber implies that there exists an open dense of $B$ where $P$ holds then $P$ holds on a constructible set.

Hi,

I would like to understand and prove the following two "well-known" facts:

1)

If $B$ is a scheme and $P$ a property for which I know:

i) if $B=Spec(V)$ where $V$ is a complete DVR, then $P$ holds on an open subset of $B$

ii) $P$ is true on a constructible set of $B$

then $P$ holds on an open subset of $B$.

2)

Assume $B$ integral. If $P$ true on the generic fiber implies that there exists an open dense of $B$ where $P$ holds then $P$ holds on a constructible set.

Hi,

I would like to understand and prove the following two "well-known" facts:

1)

If $B$ is a scheme and $P$ a property for which I know:

i) if $B=Spec(V)$ where $V$ is a complete DVR, if $P$ holds on the special point then it holds on the generic point of $B$

ii) $P$ is true on a constructible set of $B$

then $P$ holds on an open subset of $B$.

2)

Assume $B$ integral. If $P$ true on the generic fiber implies that there exists an open dense of $B$ where $P$ holds then $P$ holds on a constructible set.

sorry, by "propriety" I meant "property"
Source Link
uuuk
uuuk
  • 1
  • 1

Hi,

I would like to understand and prove the following two "well-known" facts:

1)

If $B$ is a scheme and $P$ a proprietyproperty for which I know:

i) if $B=Spec(V)$ where $V$ is a complete DVR, then $P$ holds on an open subset of $B$

ii) $P$ is true on a constructible set of $B$

then $P$ holds on an open subset of $B$.

2)

Assume $B$ integral. If $P$ true on the generic fiber implies that there exists an open dense of $B$ where $P$ holds then $P$ holds on a constructible set.

Hi,

I would like to understand and prove the following two "well-known" facts:

1)

If $B$ is a scheme and $P$ a propriety for which I know:

i) if $B=Spec(V)$ where $V$ is a complete DVR, then $P$ holds on an open subset of $B$

ii) $P$ is true on a constructible set of $B$

then $P$ holds on an open subset of $B$.

2)

Assume $B$ integral. If $P$ true on the generic fiber implies that there exists an open dense of $B$ where $P$ holds then $P$ holds on a constructible set.

Hi,

I would like to understand and prove the following two "well-known" facts:

1)

If $B$ is a scheme and $P$ a property for which I know:

i) if $B=Spec(V)$ where $V$ is a complete DVR, then $P$ holds on an open subset of $B$

ii) $P$ is true on a constructible set of $B$

then $P$ holds on an open subset of $B$.

2)

Assume $B$ integral. If $P$ true on the generic fiber implies that there exists an open dense of $B$ where $P$ holds then $P$ holds on a constructible set.

Source Link
uuuk
uuuk
  • 1
  • 1

well known facts on openness condition

Hi,

I would like to understand and prove the following two "well-known" facts:

1)

If $B$ is a scheme and $P$ a propriety for which I know:

i) if $B=Spec(V)$ where $V$ is a complete DVR, then $P$ holds on an open subset of $B$

ii) $P$ is true on a constructible set of $B$

then $P$ holds on an open subset of $B$.

2)

Assume $B$ integral. If $P$ true on the generic fiber implies that there exists an open dense of $B$ where $P$ holds then $P$ holds on a constructible set.