568 reputation
38
bio website normalesup.org/~robert/pro
location Bordeaux
age 30
visits member for 2 years, 3 months
seen Dec 19 at 0:27

Research in elliptic curve cryptology, Inria Bordeaux and Institut de Mathématiques de Bordeaux.


Oct
28
comment Elliptic Curves with CM and Class Field Theory
Sorry, I missed your comment! It comes from the fact that all isogenies of degree $m$ starting from $E_1$ will give you an elliptic curve $E_3$ with endomorphism ring of conductor a divisor of $m$, so in particular $\mathrm{End}(E_3) \supset \mathcal{O}$. This means that $E_3$ is rational over $F$, so the isogeny is rational over $F$. In particular the Galois action is of the form $\lambda \mathrm{Id}$ on the $m$-torsion; but since we have a rational point $\lambda=1$.
Oct
22
comment Is the regularity of finitely generated rings decidable?
@Yasuda: you can do Gröbner basis over R when you know how to do linear algebra over R (see for instance the survey "Grobner Bases with Coefficients in Rings" by Franz Paue). So in particular when R is an euclidean domain like $\mathbb{Z}$ (of course in practice it will be a lot slower than over a field, and over fields Gröbner basis computation can be quite long already...) At least over $\mathbb{Z}$ it is implemented by Singular (hence Sage) and Magma.
Sep
23
awarded  Yearling
Apr
21
awarded  Mortarboard
Apr
15
revised Elliptic Curves with CM and Class Field Theory
Correct a typo where I used $O_K$ instead of $O$.
Apr
15
answered Elliptic Curves with CM and Class Field Theory
Apr
15
comment Elliptic Curves with CM and Class Field Theory
Well all credits should go to Shimura for proving all the results (but for elliptic curves I guess everything was already known by Deuring!), and Streng for a nice exposition.
Apr
14
awarded  Necromancer
Apr
14
awarded  Yearling
Apr
14
awarded  Revival
Apr
14
comment Elliptic Curves with CM and Class Field Theory
@Will Sawin: you are in fact both correct, $K(j(E))$ is the subfield of the ray class field that corresponds to the ring class field; I provided more details in my answer below.
Apr
14
answered Elliptic Curves with CM and Class Field Theory
Apr
11
comment Non split extension isomorphic (as a group) to a split extension
@Yves: thanks for the reference! There is another infinite example here mathoverflow.net/a/42184/26737
Apr
11
comment Non split extension isomorphic (as a group) to a split extension
@Robinson: but $(\Z/2\Z) \times A_5$ is not isomorphic as a group to $SL(2,5)$, no?
Apr
10
revised Defining isogenies over smaller fields
(minor typo)
Apr
10
asked Non split extension isomorphic (as a group) to a split extension
Aug
23
awarded  Scholar
Aug
23
accepted What are the local properties of schemes preserved under global sections?
Aug
22
comment What are the local properties of schemes preserved under global sections?
Yes but as Will pointed out, connectivity is not a local property, so that's why I used locally noetherian instead. But this is a good point: if a local property fails for the global sections of a non affine scheme, is there any sort of additional global property that makes it work?
Aug
21
comment What are the local properties of schemes preserved under global sections?
Yes you are right of course! I just wanted to add another example than reduced, that's why I gave the integrality example. One could correct this as follows: a noetherian ring whose stalks are integral is a product of domain. This is a local condition, and so if I am not mistaken a "locally integral" locally noetherian scheme has global sections a product of domains also.