All Questions
11 questions from the last 30 days
5
votes
2
answers
378
views
Are there integer solutions of $m^4+m^2n^2+n^4=k^2$?
The recent question about Sets of integers with same sum and same sum of reciprocals, with its wealth of solutions, raises naturally the question: Can we require all those numbers to be squares? Of ...
- 13.4k
4
votes
1
answer
183
views
About the reduction type of the Kodaira symbol of elliptic curves defined over p-adic local fields
Let $K$ be a finite extension of $\mathbb{Q}_p$, and let $E$ be an elliptic curve defined over $K$. Tate's algorithm can be used to compute the Kodaira symbol of the reduction type of $E$.
However, I ...
- 77
1
vote
1
answer
121
views
Rational functions on elliptic curves over global fields with given support
Let $E$ be an elliptic curve over a global field $k$. Let $x_1, \dots, x_r$ be a set of generators of $E(k) / E(k)_{tor}$ (or more generally, a $\mathbb Q$-basis of $E(k)_{\mathbb Q}$), and let $x_0$ ...
- 77
2
votes
1
answer
125
views
Questions about elliptic curves with level-$n$ structure
Let $n$ be a positive integer, which is $4$ or a prime number $l$.
Let $E$ be an elliptic curve defined over a number field $K$.
Assume that all the $n$-torsion points of $E$ are defined over $K$, i.e....
- 77
2
votes
0
answers
123
views
Polynomial discriminant equation
This is a fairly straightforward question, and I am hoping a definitive answer exists.
Does there exist a quadratic form $A \in \mathbb{C}[x_1, x_2, x_3, x_4]$ and a cubic form $B \in \mathbb{C}[x_1, ...
- 27k
0
votes
0
answers
132
views
How near are a groupoid and its 'preorderification'?
As remarks, a groupoid is a category with only (categorical) isomorphisms as its morphisms and a preorder is a category only having one morphism between each object. If we choose one isomorphism by ...
6
votes
0
answers
135
views
Reconstructing a scheme from its quotient stack
Let $X/S$ be a scheme over a base $S$, with a group action by a nice group $G/S$ (typically $G/S$ affine smooth).
Can we reconstruct $X$ from its quotient stack $[X/G]$?
It seems that we can expect $X$...
- 645
1
vote
0
answers
89
views
Generic reducedness of geometric generic fibre
Let $f:X\to Y$ be a surjective morphism between two projective schemes over a field of characteristic $p>0$. Also assume that $X$ is smooth,$Y$ smooth & irreducible and $f_*\mathcal{O}_X=\...
- 5,986
3
votes
0
answers
64
views
p-torsion in the Tate-Shafarevich group of supersingular elliptic curves
Let $E$ be a supersingular elliptic curve over $\mathbb{F}_p(t)$. Is something known on the $p$-torsion of the Tate–Shafarevich group in this case? In particular, I would like to know if (or if known ...
- 103
3
votes
0
answers
36
views
Avoiding class/unit group computation when computing $p$-Selmer groups
Let $K$ be a number field, $S$ be a finite set of places of $K$, and $K(S,p)$ be the $p$-Selmer group of the $S$-integers of $K$, that is the set of nonzero elements of $K$ modulo $p$-th powers whose ...
0
votes
0
answers
58
views
Given $N=pq$, with what complexity we can find integer $a : q-\sqrt{q} < a <q+\sqrt{q}$?
Related to open problem and this question.
Let $N=p q$ be integer with unknown factorization.
Q1 Given $N=pq$, with what complexity we can find integer $a : q-\sqrt{q} < a <q+\sqrt{q}$?
Assume ...
- 25.4k