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Sep
23 |
awarded | Yearling |
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? |