bio  website  math.upsud.fr/~chambert 

location  Université ParisSud (Orsay)  
age  44  
visits  member for  5 years, 2 months 
seen  12 hours ago  
stats  profile views  3,593 
13h

comment 
Nth root of unity in Nth division field of abelian variety?
@JoeSilverman: Unfortunately, I made a confusion and (see Zarhin's comment above), it is $(A\times A^{\vee })^4$ which is principally polarized. 
13h

comment 
Nth root of unity in Nth division field of abelian variety?
My mistake! Sorry for the confusion and thank you for your answer and your reply to my comment. 
1d

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Nth root of unity in Nth division field of abelian variety?
It seems that one can also combine Joe Silverman's answer with your observation that $A^4$ has a principal polarization. 
1d

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Nth root of unity in Nth division field of abelian variety?
But one knows (“Zarhin's trick”) that $A^4$ has a principal polarization. Since $K(A[n])=K(A^4[n])$, this implies that the result holds in general! 
Jun 12 
comment 
When does a modular form satisfy a differential equation with rational coefficients?
@DrorSpeiser: You're right, sorry. I misunderstood your question. 
Jun 6 
comment 
discrete valuation ring and ring of witt vectors
Notation: In the context of Witt vectors, the field with $p$ elements should definitely not be denoted by $\mathbb Z_p$! 
Jun 2 
awarded  Nice Answer 
Jun 1 
answered  Solving algebraic problems with topology 
May 14 
comment 
Group schemes, adeles, double cosets, and étale cohomology
In my paper with Yuri Tschinkel, Torseurs arithmétiques et espaces fibrés, we have a similar description (Proposition 1.2.6). NB. As remarked by Philippe Gille, there is a slight mistake there, that we consider torsors which are locally trivial for the Zariski topology, without saying so. 
May 11 
comment 
Irreducible/prime/indivisible elements
The product of <= 1 field does not admit prime elements. 
Apr 24 
comment 
Constants sheaves on an open subset
Actually, the formulation of the question is incorrect, which led to the two different answers. You write that $\mathbb Z_U$ is a sheaf on $U$, while $F$ is a sheaf on $X$; so $\mathop{\rm hom}(\mathbb Z_U,F)$ does not make sense. You must either restrict $F$ to $U$ or extend $\mathbb Z_U$ to $X$. In the first case, the answer is yes (Zhen Lin's comment), and in the second it depends on the choice of an extension (direct image or extension by zero). 
Apr 22 
comment 
Base change of regular schemes
And if you want an equalcharacteristic example, take $R=\mathbf C[[t]]$ and $X$ be the closed subscheme of $\mathbf A^2_R$ defined by $xy=t$; it is regular, but its base change to $\mathbf C[[t^{1/2}]]$ is not. 
Apr 20 
comment 
Must an algebraic variety with trivial tangent bundle be an abelian variety?
And no if you don't assume some properness condition. 
Apr 18 
revised 
Reference for a lemma on étale maps
Typo. tale>étale 
Apr 17 
comment 
Reference for a lemma on étale maps
With all due respect to the established litterature, the Stacks project cannot be considered less respectable than anything else published. 
Apr 15 
comment 
Interpretation of the monomorphism $H^2(\pi_1(X),\mathbb{Z}) \rightarrow H^2(X,\mathbb{Z})$
What about removing the zerosection and considering its fundamental group? 
Apr 15 
awarded  Yearling 
Apr 12 
comment 
The resultant and the ideal generated by two polynomials in $\mathbb{Z}[x]$
A prime $p$ divides the resultant if they have a common root mod $p$ or if both of their degrees strictly decrease by reduction mod $p$. In some sense, the resultant behaves better if it is understood as an invariant of pairs of homogeneous polynomials (of given degrees). So there is a good reason that the resultant of $3x+1$ and $3x+2$ vanishes mod $3$. 
Apr 6 
awarded  Necromancer 
Apr 3 
comment 
Valuations on tensor products
The possibility of the construction ask for by Weizhe Zheng is called amalgamation property (AP) by model theorists. They observed its importance in mathematics hence studied its consequences in general algebraic structures such as fields, ordered groups, valued fields... Since ACVF plays a large rôle in applied model theorists, there should not be a surprise that these mathematicians know such facts. As shown in model theory, AP follows from the fact that the modelcompanion satisfies quantifier elimination. In the present case, the modelcompanion is ACVF and satisfies QE by Robinson. 