bio | website | math.univ-toulouse.fr/… |
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location | Toulouse | |
age | 43 | |
visits | member for | 3 years, 2 months |
seen | Sep 21 at 10:18 | |
stats | profile views | 2,097 |
Chercheur au CNRS, working in Toulouse.
I don't usually comment or answer questions from anonymous users.
Aug 25 |
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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 |
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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 |
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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 |
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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 |
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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 |
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Are there perverse sheaves on abelian varieties with small Euler characteristic?
Isn't $d=g$ in your last statement ? |
Apr 1 |
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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 |
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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 |
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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 |
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A naive algebraic geometry question
See Hartshorne, Ex. III.4.2, p. 222 (Chevalley's theorem). |
Mar 12 |
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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 |
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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 |
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Chow ring of two varieties
About this, see Ex. IV.4.10 in Hartshorne. |
Mar 9 |
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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 |
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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 |
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Formal completion of the normal bundle
@Will Savin: what do you mean by 'the completion is a bundle' ? |
Mar 8 |
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Formal completion of the normal bundle
PS The above is only valid in char. 0 because it uses the exponential map. |