bio | website | normalesup.org/~robert/pro |
---|---|---|
location | Bordeaux | |
age | 30 | |
visits | member for | 2 years, 3 months |
seen | Dec 19 at 0:27 | |
stats | profile views | 87 |
Research in elliptic curve cryptology, Inria Bordeaux and Institut de MathÃ©matiques 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. |