bio  website  math.upsud.fr/~chambert 

location  Université ParisSud (Orsay)  
age  44  
visits  member for  5 years 
seen  22 hours ago  
stats  profile views  3,478 
1d

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. 
Apr 3 
comment 
Valuations on tensor products
Isn't it the content of Exercise 2 of Bourbaki, AC VI (Valuations), §2 (page 167), which, however, is stated in the language of “places”? 
Apr 3 
awarded  Nice Answer 
Apr 3 
answered  Why is differential Galois theory not widely used? 
Mar 31 
comment 
A stronger version of Fermat's last theorem
... and that it is false is due to Lander & Parkin ($m=5$, $n=4$) and Elkies ($m=4$, $n=3$). 
Mar 31 
revised 
Mathematicians wearing hats on arbitrary total orders
Typo. $sim$ > $\sim$ 
Mar 30 
reviewed  Approve A question about the divisibility of sum of 2 consecutive primes 
Mar 27 
answered  Texts about Dwork's work 
Mar 20 
comment 
Stokes theorem with corners
See also Serge Lang's book on Fundamentals of differentiable geometry (Chapter XVII, §3). 
Mar 19 
comment 
Homotopy Type Theory: What is it?
@IianSmythe, in the same vein as Hurkyl's comment, Set theory allows you to ask whether pi (defined as you wish, coded as a set, respecting strictly the pseudo a conventions we are used to) is a group. Or whether 3 is a topology (it is...). 
Mar 17 
awarded  Nice Answer 