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1d

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Pushout and nonreduced schemes
I still don't really have ideas (although I am rather pessimistic), but I now wonder: why do you require the diagram to be cartesian? Usually cocartesian diagrams are not cartesian, and there is no reason to require that a pushout diagram be. 
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Idempotent fractional ideals of a Noetherian domain
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Idempotent fractional ideals of a Noetherian domain
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Idempotent fractional ideals of a Noetherian domain
Great, thanks! I should have tried such an example... 
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accepted  Idempotent fractional ideals of a Noetherian domain 
2d

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Idempotent fractional ideals of a Noetherian domain
Yes I tried, but there are several triples $(A,I,M)$ (ring, ideal, f.g. module) that one can try and none gave the result. For instance taking $A=R+J$ and $I=M=J$ I could prove that $R\subset J$ but then?... 
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Idempotent fractional ideals of a Noetherian domain
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asked  Idempotent fractional ideals of a Noetherian domain 
Apr 16 
answered  “Resume de cours” by J. Tits 
Apr 4 
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Subcategories of abelian categories generated by finitely many objects
Why should one want the abelian closure to be closed under taking extensions? If this condition is not required, it seems to me that one gets a subabelian category with exact inclusion (which is fine enough) but maybe not closed under isomorphisms. 
Mar 28 
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A quotient stack question
@ACL: in fact normalization commutes with smooth localization, hence is welldefined for Artin stacks. This is proved in Laumon and MoretBailly's book. 
Mar 21 
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Is there any rational curve on an Abelian variety?
@Felipe Voloch: but then you end up using the fact that you wanted to prove (that a map from $P^1$ to an ab. var. is constant). 
Jan 20 
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Has anyone found an error in an early version of Neukirch?
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Jan 20 
awarded  Necromancer 
Jan 19 
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Has anyone found an error in an early version of Neukirch?
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Jan 19 
revised 
Has anyone found an error in an early version of Neukirch?
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Jan 19 
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Has anyone found an error in an early version of Neukirch?
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Jan 18 
answered  Has anyone found an error in an early version of Neukirch? 
Jan 10 
awarded  Popular Question 
Jan 3 
awarded  Nice Question 