2,406 reputation
1129
bio website perso.univ-st-etienne.fr/…
location Saint-Etienne, France
age 32
visits member for 3 years
seen 5 hours ago

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 $E_f=\mathbb{Q}$?