History of tag 04UT
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changed the statement and the proof
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2011-08-11 |
f496b59 |
LaTeX: \Sch
Introduced a new macro
\def\Sch{\textit{Sch}}
and replaced all the occurences of \textit{Sch} with \Sch.
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changed the statement
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2010-07-02 |
4b0dbcd |
Quotient stacks
Finished the work started in commit
6bbac683b9434c98c2ba3a73dc269a8f0116cc2b
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assigned tag 04UT
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2010-07-01 |
f27a567
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Tags: Added new tags
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created statement with label lemma-compare-torsors in examples-stacks.tex
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2010-07-01 |
f396b03 |
The stack of torsors
There are many different possible definitions for the stack of
torsors for a group algebraic space G over a base B. You can
look at principal homogeneous spaces for the fpqc topology, or,
and this is more natural for us, look at fppf G-torsors. One
reason this is natural is that you get the same thing as looking
at G-torsors where you think of G as a sheaf!
If G is a group scheme over a scheme, then you could also just
look at those fppf G-torsors which are representable. Of course
this is somehow completely the wrong thing to do, but on the
other hand it is what comes natural since we know more about
schemes than about algebraic spaces.
We try to discuss all the possible variants extensively in a
section in the chapter "Examples of Stacks". In the future we
will add some lemmas/propositions/theorems saying that if G has
reasonable properties then these stacks all agree.
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