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Mar
18
comment Does X(13) have potentially good reduction at 13?
Indeed $J_1(13)$ has good reduction over $\mathbf{Q}(\zeta_{13})$ (see my comment to @znt's answer). Actually over that number field $J_1(13)$ is isogenous to the product of two conjugate elliptic curves defined over $\mathbf{Q}(\sqrt{13})$. These elliptic curves have been determined in the article "Q-curves and their Manin ideals" by Josep González and Joan-C. Lario.
Mar
18
comment Does X(13) have potentially good reduction at 13?
According to Katz-Mazur, Deligne and Rapoport showed that for $p$ prime, the abelian variety $J_1(p)/J_0(p)$ has good reduction over $\mathbf{Q}(\zeta_p)$. I wonder what can be said about $J(p)/J_0(p)$.
Mar
16
comment Does X(13) have potentially good reduction at 13?
Thanks for answering my question. For the cedilla the simplest is copy&paste, but I'm not really sensible to it
Mar
16
comment Does X(13) have potentially good reduction at 13?
The Jacobian $J(13)$ admits as a factor $J_0(169)^+$, which is a 3-dimensional variety isogenous to $A_f$, where $f \in S_2(\Gamma_0(169))^+$ is a newform with coefficients in $\mathbf{Q}(\zeta_7)^+$. Does this $A_f$ have potential good reduction at $13$?
Jan
12
comment Which vector spaces are duals ?
@silvascientist. It is $\mathbf{R}^{(\mathbf{R})}$, not $\mathbf{R}^{\mathbf{R}}$, which is isomorphic to $\mathbf{R}^{\mathbf{N}}$. The vector space $\mathbf{R}^{\mathbf{R}}$ has dimension $2^\mathfrak{c}$ by Erdős-Kaplansky.
Nov
22
comment BSD and congruent numbers
If I recall correctly the full BSD conjecture is known for the curves $E_p$ with $p$ prime $\equiv 3 \pmod{8}$ (these have rank 0). This was known before Bhargava-Shankar, see the work of Coates-Wiles and Rubin on CM elliptic curves.
Nov
22
comment BSD and congruent numbers
Do you mean the conjecture on the rank or the full BSD conjecture? I don't think it's known that the full BSD holds for a positive proportion of elliptic curves.
Nov
19
comment Examples of seemingly elementary problems that are hard to solve?
arxiv.org/abs/1511.04932v1
Nov
19
comment Not especially famous, long-open problems which anyone can understand
A proof of the conjecture is on arxiv arxiv.org/abs/1511.04932v1
Nov
4
accepted Labeling edges of an icosahedron with sum constraints
Nov
4
revised Labeling edges of an icosahedron with sum constraints
edited body
Nov
4
comment Labeling edges of an icosahedron with sum constraints
Thanks. This could actually be a variant of the original puzzle: maybe there is a nice symmetric solution allowing repetitions.
Nov
4
revised Labeling edges of an icosahedron with sum constraints
minor change in the second question
Nov
4
comment Labeling edges of an icosahedron with sum constraints
You're right. What is the smallest $N$ such that the labels are distinct and all $\leq N$ in absolute value? I guess there are algorithms to answer this kind of question.
Nov
4
comment Labeling edges of an icosahedron with sum constraints
Thanks a lot for your computations. It is still possible that there exists a distinct labeling which works, but according to your result it won't be as symmetric as in the cube case...
Nov
4
revised Labeling edges of an icosahedron with sum constraints
added 176 characters in body
Nov
3
revised Labeling edges of an icosahedron with sum constraints
added 119 characters in body
Nov
3
asked Labeling edges of an icosahedron with sum constraints
Oct
30
comment Dimension of infinite product of vector spaces
@Pierre-YvesGaillard Thanks, corrected.
Oct
30
revised Dimension of infinite product of vector spaces
added 6 characters in body