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# Defining orbit schemes

I'm wondering if it is possible to define the following kind of scheme:

Suppose X is a scheme and G is a subgroup of the endomorphism group of
X. Define for each x in X the orbit of x under G
[x] := { gx : g in G }.
Now define the set of orbits of X under G
Y := { [x] : x in X }.

My question is this: Is there a natural way of giving Y a structure of
scheme using the scheme structure of X?

If this is already a well-studied topic, can someone please point me to
where I may look this up?

Thanks.

--

-kira

Nov 10 '07 #1
2 1141
On 2007-11-09 22:12:41 -0500, Kira Yamato <ki*****@earthlink.netsaid:
I'm wondering if it is possible to define the following kind of scheme:

Suppose X is a scheme and G is a subgroup of the endomorphism group of
X. Define for each x in X the orbit of x under G
[x] := { gx : g in G }.
Now define the set of orbits of X under G
Y := { [x] : x in X }.

My question is this: Is there a natural way of giving Y a structure of
scheme using the scheme structure of X?

If this is already a well-studied topic, can someone please point me to
where I may look this up?

Thanks.
Sorry! I notice right away I've posted this on the wrong newsgroup!

--

-kira

Nov 10 '07 #2
Kira Yamato wrote:
On 2007-11-09 22:12:41 -0500, Kira Yamato <ki*****@earthlink.netsaid:
>I'm wondering if it is possible to define the following kind of scheme:

Suppose X is a scheme and G is a subgroup of the endomorphism group of
X. Define for each x in X the orbit of x under G
[x] := { gx : g in G }.
Now define the set of orbits of X under G
Y := { [x] : x in X }.

My question is this: Is there a natural way of giving Y a structure of
scheme using the scheme structure of X?

If this is already a well-studied topic, can someone please point me to
where I may look this up?

Thanks.

Sorry! I notice right away I've posted this on the wrong newsgroup!
That explains why I had no idea what you were talking about ;-)

Nov 10 '07 #3

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