bio | website | perso.univ-st-etienne.fr/… |
---|---|---|
location | Saint-Etienne, France | |
age | 32 | |
visits | member for | 3 years |
seen | 5 hours ago | |
stats | profile views | 1,447 |
I am currently a Maître de Conférences in Saint-Étienne, in France. I am particularly interested in Number Theory and Arithmetic Geometry.
Oct 18 |
reviewed | Approve suggested edit on Guess A Property Of The Integral Average Value Function |
Oct 17 |
comment |
“Algebraic” topologies like the Zariski topology?
Do buildings attached to (say) a Coxeter group enter your question or you really want something "topological" and the combinatorial aspect of buildings somehow deviates? |
Oct 16 |
reviewed | Approve suggested edit on Is there a standard notation for binary relations in category theory? |
Oct 16 |
reviewed | Approve suggested edit on Analytic extension of the exterior Newtonian potential into the domain |
Oct 16 |
reviewed | Reject suggested edit on Establishing an upper bound for a dyadic average of a function in $ {L^{p}}([0,1)) $ |
Oct 11 |
reviewed | Approve suggested edit on How to memorise (understand) Nakayama's lemma and its corollaries? |
Oct 10 |
comment |
If the direct image of f preserves coherent sheaves on noetherian schemes, how to show f is proper?
@Olivier: Ah, yes, I see - you're right. Thanks! |
Oct 10 |
comment |
If the direct image of f preserves coherent sheaves on noetherian schemes, how to show f is proper?
@OlivierBenoist: Just another small question: do you really need that a coherent sheaf can be extended (which I agree is true, of course)? After all, in your situation, what you only need is that it can be restricted (preserving coherence), no? If $f: X\to Y$ is as above and you want to prove it proper (local condition), pick a point $y\in Y$, restrict $f$ to $X_0=f^{-1}(\mathrm{Spec}(\text{local containing }y))$ and get that $f\vert X_0 :X_0\to \mathrm{Spec}(\text{this local})$ is proper, hence $f$ is proper. No? |
Oct 10 |
comment |
If the direct image of f preserves coherent sheaves on noetherian schemes, how to show f is proper?
@Olivier: nice proof, but I'm missing something on your reduction step towards finiteness of $Z$: do you ask something to the function $f\in\mathcal{O}_{\overline{X},z}$ (which you might call $g$, you already had an $f$ around, right? ) or simply not to vanish? What if I take $g=1$ and have $\overline{X},Z,X$ empty? Am I producing nonsense? |
Oct 7 |
comment |
why haven't certain well-researched classes of mathematical object been framed by category theory?
@ Martin: Without any provocative aim, but what for? I am quite categorically-inclined, or like to think that I am, but is this interpretation of any use for - say - proving Boltzano-Weierstrass or Lagrance Mean Value Theorem? If the answer is yes, do you have any reference? |
Oct 7 |
reviewed | Reject suggested edit on What polygons can be shrinked into themselves? |
Oct 2 |
awarded | Yearling |
Oct 1 |
awarded | Good Answer |
Oct 1 |
revised |
What is the most useful non-existing object of your field?
added 10 characters in body |
Oct 1 |
comment |
What is the most useful non-existing object of your field?
Ah, yes, that is what I meant... |
Sep 30 |
awarded | Explainer |
Sep 30 |
awarded | Nice Answer |
Sep 29 |
answered | What is the most useful non-existing object of your field? |
Sep 25 |
comment |
Is there an analog of the Birch/Swinnerton-Dyer conjecture for abelian varieties in higher dimensions?
In your question, you ask about Abelian Varieties and on that direction Joe Slverman's answer is indeed very complete (and accepted, as I see). But "most" of BSD has been generalized to more general varieties, without the need of any group structure, mainly by Bloch and Kato. So I wonder whether you are intentionally focusing on Abelian Varieties or if you were interested in generalizations to any sort of higher domensional gadhets. |
Sep 23 |
comment |
Adelic open image for modular forms?
@David: as far as I understand, you are looking for a generalization both in the weight and in letting the coefficient field be bigger than $\mathbb{Q}$. Why not just sticking to $k\geq 2$ but $E_f=\mathbb{Q}$? |