5,926 reputation
2040
bio website math.u-psud.fr/~chambert
location Université Paris-Sud (Orsay)
age 43
visits member for 4 years, 9 months
seen 22 hours ago

Dec
30
comment The etale fundamental group of a field
@ChandanSinghDalawat: The two volumes have been republished as a single one (with a new chapter): cassini.fr/#algebre_et_theories_galoisiennes
Dec
30
reviewed Approve The etale fundamental group of a field
Dec
30
comment Completion of a local ring of a curve
On the other hand, the hypothesis that $k$ be algebraically closed is not necessary. For example, assuming that the residual extension $k\to A/\mathfrak m$ is finite and separable, one can use Hensel's lemma to lift the residue field $A/\mathfrak m$ into a subfield of $\widehat{A_{\mathfrak m}}$.
Dec
30
revised Completion of a local ring of a curve
typo. thenor -> then for
Dec
30
reviewed Edit Companion to theoretical physics for working mathematicians
Dec
30
revised Companion to theoretical physics for working mathematicians
Adding HB Callen wonderful book on Thermodynamics (the only one I know with deals with the subject from a mathematical point of view)
Dec
25
answered Link: Serre's intersection formula <-> Bloch-Quillen Thm / When only intersecting divisors, is there 'shorter' approach of proof known?
Dec
25
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 semi-abelian. As Bosch-Lütkebohmert-Raynaud 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 set-theoretic 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 p-adic 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 non-degenerate 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 baby-case.
Dec
10
answered How to prove embedded copies of a curve using different base points in its Jacobian are algebraically equivalent