1,331 reputation
714
bio website math.univ-toulouse.fr/…
location Toulouse
age 43
visits member for 3 years, 2 months
seen Sep 21 at 10:18
Chercheur au CNRS, working in Toulouse. I don't usually comment or answer questions from anonymous users.

Aug
25
comment Rational points techniques on curves not using their Jacobian
The method of Kim is very interesting but he can only prove Siegel's theorem for the projective line, as far I can see. In that case, (much) more elementary proofs can be made quite effective (see Silverman's book on elliptic curves) but even this does not give a method to find all the rational points on a curve.
Aug
24
comment Rational points techniques on curves not using their Jacobian
The very conjectural "effective Mordell conjecture" (see Astérisque 183) would provide such a method. The analog of this conjecture is proven over function fields (proofs by Arakelov and Szpiro) and such a method is thus available over function fields. Over number fields, I don't know any method that does not use the Jacobian.
Aug
24
comment Hermitian metric on $f_*(\Omega_{X/X_{can}}^{n-k})$
What is $X_{\rm can}$ exactly ? Also, is it clear that $\Omega_{X/X_{\rm can}}$ is locally free ? If so, why is $f_*(\Omega_{X/X_{\rm can}})$ locally free ? If it is not, then what do you mean by hermitian metric on that object ? (sorry if all this is standard).
Aug
22
awarded  Yearling
Jul
2
awarded  Curious
Jun
20
comment splitting of the Hodge filtration
I think the OP means: "When is the canonical Hodge splitting already defined over $k$ ?". This happens rarely and the failure to split over $k$ is basically encoded in the Mumford-Tate group, about which there are many deep conjectures. For instance if $X$ is a CM abelian variety and $k$ contains the Galois closure of the CM field, then the sequence splits (and the Mumford-Tate group is a torus).
May
14
comment Ampleness of Hodge bundles over complex curves
@Jason Starr. Thank you for your remark. I would expect something like that but I cannot find any coherent bibliographical reference for this kind of thing.
May
14
asked Ampleness of Hodge bundles over complex curves
Apr
1
comment Are there perverse sheaves on abelian varieties with small Euler characteristic?
Isn't $d=g$ in your last statement ?
Apr
1
comment Is it possible to prove Mordell's conjecture geometrically?
This is a good question. It has always struck me that the only known proofs of the Mordell conjecture over number fields, as well as of the Manin-Mumford conjecture require arithmetic models. The only thing I know in the "purely complex" (or "geometrical") direction is Zannier-Pila's approach to Manin-Mumford (but not Mordell...), which still requires arithmetics, but less so than Raynaud's (or Ullmo-Szpiro-Zhang, or Pink-R.'s).
Mar
23
comment Chow ring of a $\mu_2$-gerbe
I have only recently come across your question. Do you actually mean a $\mu_2$-torsor ?
Mar
23
comment Inequality regarding sum of gaussian on lattices
It might be interesting to consider the special case where the lattice comes from the fractional ideal of a number field. Then you could use the functional equation of the theta function. See arxiv.org/pdf/math/9802121v3.pdf or math.univ-toulouse.fr/~rossler/mypage/pdf-files/…
Mar
21
comment A naive algebraic geometry question
See Hartshorne, Ex. III.4.2, p. 222 (Chevalley's theorem).
Mar
12
comment Chow ring of two varieties
This is true for varieties having an 'algebraic cellular decomposition'. See Example 19.1.11 in Fulton, Intersection Theory, p. 378.
Mar
12
comment Given a morphism of schemes, when does bijective + isomorphic tangent spaces = isomorphism?
See Lemma 2.4, p. 172 in Cornell-Silverman, 'Arithmetic Geometry' (article by Milne) for a statement in the direction of what you are looking for.
Mar
11
comment Chow ring of two varieties
About this, see Ex. IV.4.10 in Hartshorne.
Mar
9
comment Formal completion of the normal bundle
I think you need to complete the symmetric algebra along the augmentation ideal to get the iso. of $k$-algebras you mention.
Mar
8
comment Formal completion of the normal bundle
@Will Savin: PS: The OP considers the formalisation of $Z$ inside $N_{Z/X}$, not the formalisation of $N_{Z/X}$ (unless I have been completely mislead).
Mar
8
comment Formal completion of the normal bundle
@Will Savin: what do you mean by 'the completion is a bundle' ?
Mar
8
comment Formal completion of the normal bundle
PS The above is only valid in char. 0 because it uses the exponential map.