1,301 reputation
617
bio website perso.univ-rennes1.fr/…
location Rennes
age 38
visits member for 4 years, 4 months
seen 4 hours ago

Aug
29
revised Affine hulls and base change
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Aug
28
revised Affine hulls and base change
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Aug
28
comment Affine hulls and base change
Well, I may be wrong then. I'm editing my answer accordingly.
Aug
27
comment Affine hulls and base change
Damned! I had overlooked that subtlety. At the moment I don't know how to argue -- do you have an example of a sheaf of modules on a scheme that does not embed into a quasi-coherent one ? What about a sheaf of the form $f_*O_X$?
Aug
27
comment Affine hulls and base change
Dear Fred, I don't know a place where you can find this explained in full without the qcqs hypothesis. But you can find the lemma on existence of largest quasicoherent submodules in the Stacks Project under Lemma Tag 01QZ and then check for yourself that 1) in the case of a sheaf of algebras this largest thing is a subalgebra and 2) the Spec of this satisfies the universal property of the affine hull. For question B, sorry I misread. But I don't quite see what kind of condition on $S'\to S$ could do.
Aug
27
answered Affine hulls and base change
Jul
4
comment A construction of the Hilbert-Chow morphism
One source is 'Local properties and Hilbert schemes of points' by Fantechi and Göttsche, in the volume 'Fundamental Algebraic Geometry' for the 2003 Trieste School, published by AMS.
Jul
3
comment Fantastic properties of Z/2Z
Yes, I know that song, it's fantastic.
Jul
2
awarded  Curious
Jun
28
revised Descent of functions along finite birational morphisms
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Jun
28
revised Descent of functions along finite birational morphisms
added 95 characters in body
Jun
28
comment Descent of functions along finite birational morphisms
ps: in Olivier's note the result is the Corollary to Thm. 2.6.
Jun
28
comment Descent of functions along finite birational morphisms
Dear anon, that's a great answer! In fact I thought a bit more and found out that result about descent along pure morphisms in the 1970 CRAS note 'Descente par morphismes purs' by J.-P. Olivier (no proof there). I read also in the The Stacks Project that Mesablishvili was the first to give full proofs of such statements. On the other hand I had made no connection with Reynolds operators. Thanks for these explanations and references! That's very useful to me.
Jun
27
revised Descent of functions along finite birational morphisms
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Jun
26
comment Descent of functions along finite birational morphisms
Dear user52824, I completed the proof with your insightful suggestions. Thanks!
Jun
26
revised Descent of functions along finite birational morphisms
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Jun
26
awarded  Self-Learner
Jun
26
comment Descent of functions along finite birational morphisms
Whoops, thanks for pointing out the parasitic 'locally' in the statement of Lemma 3. As for the dominance assumption, it is in fact equivalent to S'->S being epic. As for 'strict epi', I didn't define it but it is standard, see e.g. Grothendieck's Bourbaki 190. Finally thank you for the ideas to fill in the hole in the proof, I'll edit so as to incorporate this to the answer above.
Jun
26
revised Descent of functions along finite birational morphisms
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Jun
25
revised Descent of functions along finite birational morphisms
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