1,440 reputation
715
bio website math.univ-toulouse.fr/…
location Toulouse
age 44
visits member for 3 years, 11 months
seen 14 hours ago
Chercheur au CNRS, working in Toulouse. I don't usually comment or answer questions from anonymous users.

14h
comment Is this kind of scheme integral?
For smthg related to your question, see Prop 4.3.8 p. 137 in Liu book (this shows eg that if you assume that $X$ is flat over $R$ and $X_\eta$ is integral, then so is $X$).
Jun
25
accepted CM abelian varieties over the rationals
Jun
25
comment CM abelian varieties over the rationals
Nice answer... thank you for that. I wonder why this argument does not appear in any of the usual references for the theory of complex multiplication (unless I missed something ?).
Jun
24
asked CM abelian varieties over the rationals
Jun
17
comment Projective bundle formula
(you means $X={\bf P}(E)$ in your formula) If $X$ is smooth and proper, then by Hodge decomposition the formula is the same as for singular cohomology (see Griffiths-Harris, p. 606). If $X$ is smooth but not necessarily proper then the cohomology ring might be infinite-dimensional.
May
16
comment Reference request: Cohomology of Elliptic Curves
Why is the image of $\mu_\nu$ a normal subgroup of ${\rm Gal}(K^{\rm ab}|K)$ ? Sorry if I missed something obvious.
Apr
2
comment Connected vs Irreducible Subvarieties
What about normality ?
Feb
25
comment A proper smooth surface is projective
Several classical references are given on II, §4, p. 105 of Hartshorne's book.
Jan
25
comment References for general Hasse-Weil zeta function
I do not know any other coherent reference than "facteurs locaux"....
Jan
5
comment 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
comment Quotient of a (non-linear) 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
comment 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 Zarhin-Parshin corresponds precisely to what follows from Mordell-Lang + Mazur's conjecture.
Nov
28
comment Fermat's last theorem over larger fields
See also Zarhin-Parshin, "Finiteness theorems...", p. 92 for a related conjecture (also made by Mazur).
Nov
26
comment How to see that this pairing of line bundles is multiplicative?
Do you want a canonical isomorphism (inv. under base-change) ? 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
comment 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 non-singular ?).
Nov
14
comment 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
comment 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).