bio | website | mat.ulaval.ca/hchapdelaine/… |
---|---|---|
location | Quebec city | |
age | 36 | |
visits | member for | 3 years, 8 months |
seen | 6 hours ago | |
stats | profile views | 3,174 |
Aug 11 |
comment |
On Severi's definition of the complementary correspondence
thanks for the answer. |
Aug 11 |
accepted | On Severi's definition of the complementary correspondence |
Aug 11 |
comment |
On Severi's definition of the complementary correspondence
So if we think of $T:C\rightarrow C$ as a multivalued function and $T(P)=\sum_{i} [P_i]$ (formal sum) then are you saying that $(-T)(P)=\sum_{i} [-P_i]$? |
Aug 11 |
asked | On Severi's definition of the complementary correspondence |
Aug 7 |
accepted | Explicit formula for the Poincare dual of a CM endomorphism of an elliptic curve |
Aug 7 |
comment |
Explicit formula for the Poincare dual of a CM endomorphism of an elliptic curve
Yes you are right! So this solves my question. Many thanks! |
Aug 6 |
comment |
Explicit formula for the Poincare dual of a CM endomorphism of an elliptic curve
Hi @Will. I agree with everything you said except that I don't quite see why $\Delta\cdot\Gamma$ corresponds to $[(1-\sqrt{-D})^{-1}\mathcal{O}_K:\mathcal{O}_K]$ |
Aug 6 |
comment |
Explicit formula for the Poincare dual of a CM endomorphism of an elliptic curve
I thought a bit a bout my problem and now I realized that the way I set it up is probably not ideal. It is probably better to work with homology since then one can make pictures. The group $H_2(E,\mathbf{Z})$ has $3$ natural $\mathbf{Z}$-linearly independant elements, namely $E_1=E\times\{0\}$, $E_2=\{0\}\times E$ and $\Delta$ (the diagonal). Intuitively we should have $E_2\cdot \Gamma=1$ and $E_1\cdot\Gamma=D$. Though the intersection $\Delta\cdot \Gamma$ seems to be more complicated to compute. |
Aug 6 |
revised |
Explicit formula for the Poincare dual of a CM endomorphism of an elliptic curve
added 114 characters in body |
Aug 6 |
revised |
Explicit formula for the Poincare dual of a CM endomorphism of an elliptic curve
added 447 characters in body |
Aug 6 |
asked | Explicit formula for the Poincare dual of a CM endomorphism of an elliptic curve |
Jul 19 |
comment |
General criterion to find a Z-basis in a fixed generating subset
Thanks, now I think I see how to prove it. The point is that multiplication on the left or the right by an invertible matrix with coefficients is Z preserves the determinant of the $k\times k$ minors. |
Jul 19 |
accepted | General criterion to find a Z-basis in a fixed generating subset |
Jul 18 |
revised |
General criterion to find a Z-basis in a fixed generating subset
added 232 characters in body |
Jul 18 |
comment |
General criterion to find a Z-basis in a fixed generating subset
no, I really meant what I wrote. |
Jul 18 |
asked | General criterion to find a Z-basis in a fixed generating subset |
Jul 18 |
awarded | Popular Question |
Jul 15 |
comment |
minimal conductors among elliptic curves with a fixed CM type
Thanks for the data. Yes my questions are closely related to asking for a "canonical Grossencharacter" of a quadratic CM field, but from what you say it seems that such an object does not really exist. |
Jul 15 |
asked | minimal conductors among elliptic curves with a fixed CM type |
Jul 15 |
comment |
On the conductor of the Groessencharacter of a CM elliptic curve
So the point is as @Cesnavicius wrote, the support of the conductor won't be bounded. |