bio | website | math.u-psud.fr/~chambert |
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location | Université Paris-Sud (Orsay) | |
age | 43 | |
visits | member for | 4 years, 4 months |
seen | Aug 29 at 8:56 | |
stats | profile views | 2,794 |
Aug 4 |
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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 |
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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 |
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A short proof for $\dim(R[T])=\dim(R)+1$
@MartinBrandenburg: The alleged counterexample of Alex was puzzling. What was wrong finally? |
Jun 19 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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. |