bio  website  math.upsud.fr/~chambert 

location  Université ParisSud (Orsay)  
age  43  
visits  member for  4 years, 8 months 
seen  9 hours ago  
stats  profile views  3,087 
2d

answered  Link: Serre's intersection formula <> BlochQuillen Thm / When only intersecting divisors, is there 'shorter' approach of proof known? 
2d

comment 
Collecting proofs that finite multiplicative subgroups of fields are cyclic.
I love this proof which furnishes an explicit generator. A slight variant of it consists in observing that if $x$ is chosen so that $x^{n/p}\neq 1$ (roughly one element over $p$ will do the job), then $x^{n/q}$ is of exact order $q$. The rest is as in Paul's answer. 
Dec 23 
reviewed  Approve Where is the Erdős–Rado theorem stated in Erdős and Rado's Bull AMS paper? 
Dec 21 
comment 
Pathological behavior of Lie algebra under a map of abelian schemes
Raynaud's theorem also requires that $F'$ be semiabelian. As BoschLütkebohmertRaynaud say at the end of example 7/5.9, their example shows that this hypothesis cannot be relaxed. 
Dec 21 
awarded  Enlightened 
Dec 21 
awarded  Nice Answer 
Dec 17 
reviewed  Reject nontrivial theorems with trivial proofs 
Dec 17 
comment 
Coherent cohomology of an abelian scheme and base change
Berthelot, Breen and Messing, Théorie de Dieudonné cristalline, II (LNM 930), Prop. 2.5.2 compute the De Rham cohomology of an abelian scheme  the proof uses a bit of spectral sequences. 
Dec 17 
comment 
(Affine) Schemes and the point of view of morphisms with values in a field
It depends on the settheoretic framework you place yourself. Within ZFC, you have no other option than fixing a set of fields; within a theory with classes, the morphisms from $A$ to a field will constitute a class; within Bourbaki's theory, there is a notion of an equivalence relation without mentioning an underlying set, but you will need to prove (this is easy) that this relation is "collectivisante" so that its equivalence classes form a set. 
Dec 16 
answered  padic Stein spaces 
Dec 16 
comment 
Least supersingular prime
@MichaelStoll: You're right (twice)... 
Dec 16 
answered  Least supersingular prime 
Dec 11 
comment 
How to prove that two univariate polynomials are always algebraically dependent?
Actually, the way Ma and Marinescu prove this theorem of Siegel, consists in considering the map $K[T_1,...,T_k]\to \mathscr M(X)$ induced by the $f_i$, and to show that it cannot be injective if $k>\dim(X)$ by inspecting its jets at a nondegenerate point $x$, making use of the Schwarz lemma. It is thus very close to Michael Stoll's approach which can be thought of as a kind of babycase. 
Dec 10 
answered  How to prove embedded copies of a curve using different base points in its Jacobian are algebraically equivalent 
Dec 10 
comment 
Tensor productdefinitionbalanced versus bilinear maps
Take a module $P$ which has two distinct structures of an $R$module. ($R=P=\mathbf C$ is an acceptable choice.) Then it seems that a bilinear map for the first structure is only balanced for the second one. 
Dec 8 
answered  Is the Weil–Deligne representations coming from $\ell$adic cohomology independent of $\ell$? 
Dec 3 
comment 
Is there a scheme parametrizing the closed subgroups of an algebraic group?
Take $G=\mathbf G_m^2$ (or, to keep your notation, restrict to subgroups of a maximal torus). Then connected subgroups of dimension $1$ correspond to rational lines in $\mathbf Q^2$ — the only relevant schematic structure seems to be the discrete one. 
Nov 27 
comment 
How to see that this pairing of line bundles is multiplicative?
The Deligne pairing has been studied in the mid 80s — in relation with Arakelov geometry. You could have a look at the papers of Deligne (Le déterminant de la cohomologie), MoretBailly (in Seminaires sur les pinceaux arithmétiques, Astérisque), or, for a higher dimensional generalization, Elkik (Fibrés d'intersection et intégrales de classes de Chern). All of this is in French, though. 
Nov 26 
awarded  Pundit 
Nov 25 
comment 
Fermat's last theorem over larger fields
@ACL: I forgot one hypothesis in the quoted theorem, namely that the curve has $\mathbf Q_p$ points for all primes $p$. 