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location  Rennes, France  
age  63  
visits  member for  4 years, 10 months 
seen  34 mins ago  
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1d

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Varieties acted upon faithfully by an abelian variety
Standard construction: Let $G$ be a finite subgroup of $A$ acting freely on a variety $Y$. Then $G$ (resp. $A$) acts on $A\times Y$ by the diagonal action (resp. translation on $A$), and these actions commute so $A$ acts on $X:=A\times Y/G$, and it is easy to see that this action is free. Moreover, if you choose $Y$ so that every morphism $Y\to A$ is constant (e.g. $Y$ rational) then there is no $A$equivariant morphism $X\to A$, and in particular $X$ is not a product $A\times Z$. 
2d

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Automorphisms of a differential field and transcendence degree
Perhaps I am missing something, but from the definition it seems clear that $\mathcal{E}_\Phi$ is just $\Phi(\mathcal{E})$ and is isomorphic to $\mathcal{E}$ as a (differential) field. 
May 16 
awarded  Citizen Patrol 
May 13 
answered  Degree of sum of integral elements over a UFD 
May 7 
comment 
Infinitesimal deformations of the formal group of $\mathbb{G}_m$
Oh, right. I had read the question too fast. 
May 7 
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Infinitesimal deformations of the formal group of $\mathbb{G}_m$
"The intervention of formal groups is a red herring": why is that? The question is about formal groups. 
May 7 
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Is a normal proper relative curve over a DVR projective?
@Lisa: I suppose you may do that. In a more downtoearth way, you can pick a closed point $x$ of the closed fiber $X_0$ which is in the regular locus $U$, and then a (Weil) divisor $D$ through $x$, finite over $R$. If $R$ is henselian, $D$ splits as $D'\coprod D"$ where $x$ is the only point of $D'$ in the closed fiber, so $D'\subset U$. Repeat this with one $x$ in each component of $X_0$ and take the sum of the $D'$'s: this is an ample Cartier divisor. 
May 6 
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Is a normal proper relative curve over a DVR projective?
I think the answer is also yes if $R$ is henselian, if this helps. 
May 1 
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Why are unramified maps not required to be locally of finite presentation?
For one thing, it seems reasonable that all immersions should be unramified. 
Apr 30 
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Examples of quotients by infinitesimal group schemes
The construction itself was known before: for instance it is mentioned in Mumford's Abelian Varieties. What I proved in my paper is that the resulting quotient is the Jacobian of a genus 2 fibration over $\mathbb{P}^1$. 
Apr 30 
awarded  ac.commutativealgebra 
Apr 29 
revised 
Automorphisms of complete local rings
Error corrected, pointed out by Ycor 
Apr 29 
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Automorphisms of complete local rings
@YCor: Thanks, Yves! Corrected. 
Apr 29 
answered  Automorphisms of complete local rings 
Apr 13 
answered  Fibrations of projective varieties 
Apr 11 
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Does this $\mathbb{Z}_p$algebra morphism induce a closed immersion on the generic fiber?
Take $R=\mathbb{Z}_p$, $B=$ a nontrivial finite extension of $\mathbb{Q}_p$, $f$ mapping $x$ to zero. The image of $f[1/p]$ is $\mathbb{Q}_p$ but $f\bmod p$ is surjective since $B/(p)$ is zero. 
Apr 6 
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Is a normal proper relative curve over a DVR projective?
If I remember correctly, Artin's contraction results give rise to algebraic spaces, not schemes (except, for instance, over a finite field). So, what kind of ``curve'' are we looking for? 
Apr 2 
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Writing down gerbes explicitly over the projective line
Try the gerbe of square roots of $\mathscr{O}(1)$. 
Mar 30 
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When does an algebraic space that is a torsor over a scheme have to be a scheme?
The paper cited by Ariyan (which I have not read) is presented as a simplified version of the example in Raynaud's thesis (LNM 119, XIII.3.2). See also loc. cit. VI.2.5 for Q3: if $S$ is normal and noetherian and $G$ is smooth with connected fibers on $S$, then every $G$torsor is locally quasiprojective over $S$. 
Mar 27 
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Is surjectivity for morphisms of schemes local on the domain?
It is wrong indeed. 