6,928 reputation
2646
bio website math.u-psud.fr/~chambert
location Université Paris-Sud (Orsay)
age 44
visits member for 5 years, 1 month
seen 23 hours ago

May
18
comment A question about intersection theory over non algebraically closed field
This has nothing to do with intersection theory: for the bilinear map $f\colon k^m\times k^n\to k^\ell$ to induce a morphism $\mathbf P^{m-1}\times\mathbf P^{n-1}\to\mathbf P^{\ell-1}$, you need to be sure that $f(x,y)=0$ implies $x=0$ or $y=0$ for $x,y$ with coefficients in the algebraic closure of $k$.
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 equal-characteristic 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 zero-section 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 model-companion satisfies quantifier elimination. In the present case, the model-companion 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