bio  website  math.univtoulouse.fr/… 

location  Toulouse  
age  44  
visits  member for  3 years, 5 months 
seen  59 mins ago  
stats  profile views  2,167 
Chercheur au CNRS, working in Toulouse.
I don't usually comment or answer questions from anonymous users.
55m

comment 
References for general HasseWeil zeta function
I do not know any other coherent reference than "facteurs locaux".... 
Jan 5 
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automorphisms of local rings vs local change of coordinates
I think you haven't actually stated which two objects you want to coincide. 
Dec 14 
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Quotient of a (nonlinear) algebraic group by a closed subgroup
Here is another reference: Raynaud, 'Passage au quotient par une relation d'équivalence plate', Proceedings of a conference on local fields (Driebergen, 1967), p. 82 Ex. a) (i). 
Nov 29 
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Fermat's last theorem over larger fields
Sorry, your are right, Mazur's conjecture does not quite cover your question (but it gives a partial answer). The conjecture in ZarhinParshin corresponds precisely to what follows from MordellLang + Mazur's conjecture. 
Nov 28 
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Fermat's last theorem over larger fields
See also ZarhinParshin, "Finiteness theorems...", p. 92 for a related conjecture (also made by Mazur). 
Nov 26 
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How to see that this pairing of line bundles is multiplicative?
Do you want a canonical isomorphism (inv. under basechange) ? Or would you be happy with any isomorphism ? 
Nov 19 
accepted  On a proposition in Hartshorne's paper “Ample vector bundles on curves” 
Nov 16 
awarded  Nice Question 
Nov 16 
comment 
On a proposition in Hartshorne's paper “Ample vector bundles on curves”
Thank you very much for taking the time to write this answer. If I understand your answer right, your construction is in the same line as what ulrich described in his comment. I would still like to see a proof or a counterexample to Prop. 4.1, though but if nobody provides one in the next few days I will accept your answer. 
Nov 15 
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On a proposition in Hartshorne's paper “Ample vector bundles on curves”
@ulrich. Thank you very much for this interesting comment. That settles it then, as far as (X) is concerned. Here is a possible simplification of your argument: as you write, $C\to f(C)$ must be generically separable because $H^0(A,\Omega_A)\to H^0(C,\Omega_C)$ does not vanish. Now since $C\to f_*(C)$ is also generically inseparable, it must be birational. Note that $f_*(C)$ might be singular, so its geometric genus might not be defined (or is there a way to show that it must be nonsingular ?). 
Nov 14 
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On a proposition in Hartshorne's paper “Ample vector bundles on curves”
Thank you for this reference. I had a look at Fulton's paper but I cannot find an argument in there that shows that (X) (in my post) or Prop. 4.1 is wrong in a specific situation. The counterexample of Serre that Fulton mentions is apparently a construction that appears in the very paper by Hartshorne that I am concerned with (in par. 3). It is an example of a curve and a vector bundle on it, which is not ample and yet has only positive quotients. How does all this connect to (X) or Prop. 4.1 ? 
Nov 14 
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On a proposition in Hartshorne's paper “Ample vector bundles on curves”
@Donu Arapura: $\phi$ is birational onto its image (I edited the question 30 minutes ago  you might have read the post just before that  sorry). 
Nov 14 
asked  On a proposition in Hartshorne's paper “Ample vector bundles on curves” 
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 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 MumfordTate 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 MumfordTate 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 