5,313 reputation
1736
bio website math.u-psud.fr/~chambert
location Université Paris-Sud (Orsay)
age 43
visits member for 4 years, 4 months
seen Aug 29 at 8:56

Aug
4
comment Connections between Standard, Hodge and Tate conjectures on algebraic cycles?
The Tate conjecture furnishes $\mathbf Q_\ell$-linear combinations of cycles. Is it enough?
Jul
11
awarded  Necromancer
Jul
4
comment A construction of the Hilbert-Chow morphism
See Amnon Neeman, Zero cycles in $P^n$, Adv. Math. 89 (1991), no. 2, 217–227. There is also a discussion in Section 4.3 of David Rydh's paper Hilbert and Chow schemes, symmetric powers and divided powers, math.kth.se/~dary/thesis/thesis-paperIII.pdf
Jul
2
awarded  Curious
Jun
25
comment A short proof for $\dim(R[T])=\dim(R)+1$
@MartinBrandenburg: The alleged counterexample of Alex was puzzling. What was wrong finally?
Jun
19
comment questions about the “relative fundamental group” of SGA 1 Expose XIII
Beware! Don't confuse séparé (separated) and séparable; the latter means that the geometric fibers are reduced.
Jun
13
comment Schemes over $K_s$ and over $\bar{K}$
@FelipeVoloch: bijection! I hadn't even noticed that. As would my daughter say, WTF... :-) [PS. That's quite unfortunate that the set theory we live in allows for questions which have no mathematical sense.]
Jun
13
comment Specialization Map of family of abelian varieties
@wongpin101 (followed). This continues to work if $S$ is the spectrum of a Dedekind ring. In the general case, the morphism of groups $X(S)\to X_F(F)$ is injective but has no reason to be an isomorphism. This is already the case if $S$ is not normal. And if $S$ is normal, a morphism $Spec(F)\to X$ only extends outside of a codimension 2 subset in general.
Jun
13
comment Specialization Map of family of abelian varieties
@wongpin101: I think you are missing a point in the definition of the specialization map. Let $X/S$ be an abelian scheme, where $S$ is integral, with field of fractions $F$. First assume that $S$ is the spectrum of a DVR. Then the valuative criterion of properness furnishes an isomorphism of groups $X(S) \to X_F(F)$. On the other hand, if $s$ is the special point of $S$, one has a morphism of groups (functoriality) $X(S)\to X_s(\kappa(s))$. These two properties give the specialization morphism $X_F(F)\to X_s(\kappa(s))$.
Jun
11
comment Schemes over $K_s$ and over $\bar{K}$
The answer to question 2 is obviously NO: If $X=\mathbf A^1$ is the affine line, then $X_K(K)=K$, for every field (even, ring) $K$. So $X_{K_s}(K_s)=K_s$ and $X_{\overline K}(\overline K)=\overline K$...
Jun
11
comment Étale homotopy type of non-archimedean analytic spaces
As is the underlying topological space of an elliptic curve with good reduction. In the case of degenerating families over a disk, a theorem of Berkovich states that the topology of Berkovich spaces (only) explains for the weight-0 part of the limit Hodge structure.
Jun
10
comment Equivariant motivic sheaves
@ReladenineVakalwe: Look at his webpage. His ICM address (A guide to (etale) motivic sheaves, user.math.uzh.ch/ayoub/PDF-Files/ICM2014.pdf) should be a good start! Section 4 is called "Motives over a field".
Jun
9
comment Commutative algebras whose bidual is commutative
Had you had a look at the paper On the second conjugate space of a Banach algebra as an algebra, projecteuclid.org/euclid.pjm/1103037121, by Paul Civin and Bertram Yood. They seem to give a fairly detailed study of the question. In particular, they give conditions under which the analogue of this algebra (in the Banach category) is not commutative. (It is almost never.)
Jun
7
comment group structure on (subsets of) tropicalizations of Abelian varieties
Yes and no. This question of comparing the skeleton of the elliptic curve (the canonical circle described above) with more naïve tropicalizations from embeddings is discussed in a paper of Baker, Payne and Rabinoff, Nonarchimedean geometry, tropicalization, and metrics on curves, arxiv.org/abs/1104.0320.
Jun
7
comment Local factors of Hasse-Weil zeta function - what do they have in common?
@AndreasHolmstrom: because the functional equation shows that the zeta function (a rational function) has less independent coefficients than what you would think, roughly half of it.
Jun
6
comment Are Abelian varieties (sometimes) globally $F$-split?
Recalling the definition would help...
Jun
6
answered Local factors of Hasse-Weil zeta function - what do they have in common?
Jun
6
comment group structure on (subsets of) tropicalizations of Abelian varieties
Tropicalizing just means applying the valuation map, once it makes sense. The case of semistable formal schemes also gives rise to maps to simplicial complexes associated with the special fiber, but this is a (related but) different story.
Jun
6
answered group structure on (subsets of) tropicalizations of Abelian varieties
Jun
6
comment Let $f \colon X \to Y$ be an étale morphism of schemes. If $Y$ is integral, then is $X$ integral?
@user125763: No it's not! The empty topological space is not irreducible, but some say it is connected, and the zero ring is not integral.