changed the statement
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2017-08-01 |
d9448f5 |
Reference for 04DZ.
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changed the proof
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2015-09-26 |
5359b6a |
Second proof for topological invariance etale site
This is the proof of the equivalence of etale sites under a
universal homeomorphism. The first proof uses the very delicate
arguments about comparison of sites in various forms earlier
in the chapter on etale cohomology. This material is kinda
hard to read and maybe a bit nonstandard. The new proof
is just like the proof in SGA 1 and uses the descent for
etale morphisms along surjective integral morphisms + the
topological invariance for thickenings... In fact in some
sense the new proof may very well be harder, but it seems
at least easier to break it up into parts which have meaning...
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changed the proof
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2014-01-26 |
1a25072 |
Start explaining Gabber's argument
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changed the proof
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2013-08-03 |
dba86b5 |
pell check: words starting with n, o, p, q, r, N, O, P, Q, or R
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changed the proof
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2011-06-09 |
76acad1 |
Moving lemmas for clarity
Following a suggestion of David Rydh we tried to collect results
related to universally injective unramified morphisms into one
place. We did not completely succeed, but hopefully the end
result is still an improvement!
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changed the proof
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2011-03-30 |
630c061 |
Wrap up proof
of topological invariance of X_{spaces, etale} for integral,
universally injective, and surjective morphisms. It seems to me
this is an open question when you only assume the morphism is a
universal homeomorphism... Anybody?
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changed the proof
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2011-03-29 |
ee75333 |
Bunch of changes
(1) Starting to write about thickenings of algebraic spaces
(2) Change Omega^1_{X/S} to Omega_{X/S}
(3) Introduced universal homeomorphisms for algebraic spaces
(4) If X ---> Y is a surjective, integral morphism of schemes
and X is an affine scheme, then Y is an affine scheme
(4) Topological invariance of the site X_{spaces, etale} of an
algebraic space X (proof unfinished}
In order to see that also X_{etale} is a topological invariant
we (I think) need to prove the following result: If X --> Y is a
integral, universally injective, surjective morphism of
algebraic spaces then X is a scheme if and only if Y is a
scheme. There are two proofs of this result in the literature
(one by David Rydh and one by Brian Conrad); both reduce the
result to the Noetherian case by limit arguments. I would
prefer a more direct argument...
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changed the statement and the proof
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2010-10-09 |
97a5c76 |
Begin translating etale to \'etale or \acute{e}tale (in Math mode).
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changed the proof
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2010-06-06 |
b504204 |
Etale local on the source-and-target
Absurdly detailed discussion of three different notions of what
it can mean for a property of morphisms of schemes to be etale
local on the source and target. We choose the strongest of the
three to avoid confusion that will inevitably arise when picking
one of the other two. Moreover, it will be nicely compatible
with the notion (to be introduced in the next commit) of what it
means for a property of morphisms of germs to be etale local on
the source and target.
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changed the proof
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2010-03-30 |
02cad0a |
Exclamation --> period.
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created statement with label theorem-topological-invariance in etale-cohomology.tex
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2010-03-28 |
c86d591 |
Large commit
Just trying to recover from the brain dead mistakes made over
the last few weeks. Hopefully most of it is now more or less OK.
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assigned tag 04DZ
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2010-03-28 |
c86d591
|
Large commit
Just trying to recover from the brain dead mistakes made over
the last few weeks. Hopefully most of it is now more or less OK.
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