All Questions
663 questions with no upvoted or accepted answers
0
votes
0
answers
275
views
r-torsion points on elliptic curve on finite field
Let $E(\mathbb{F}_q)$ - elliptic curve, $r$ is prime, $|E(\mathbb{F}_q)[r]| > 1$.
Let $r | q-1$. Is it true that $|E(\mathbb{F}_q)[r]| = r^2$?
- 2,576
0
votes
0
answers
385
views
Analytic rank of an elliptic curve with algebraic rank 0
Let $E$ be an elliptic curve over $\mathbb{Q}$ with algebraic rank 0. Is there any way, one can argue that the analytic rank must be even? Of course this would follow from the standard conjectures, ...
- 11
0
votes
0
answers
440
views
Foliations in positive characteristic
Ekedahl wrote about foliations in positive characteristic, over the field $\mathbb{Z}/p\mathbb{Z}$ as a subsheaf of the tangent sheaf, that are closed with respect to involution and $p$-power.
My ...
- 1
0
votes
0
answers
296
views
elliptic curves in form $y^2=x^3+p^2x$ where p is prime with rank 0
We Know that from a conjecture by Goldfeld says that half of all elliptic curves have rank zero.
Are there any known infinite families of elliptic curves in form
$y^2=x^3+p^2x$ where p is prime with ...
- 345
0
votes
0
answers
189
views
$T^2$-fibered K3 surface with involution
Let $S$ be a K3 surface and $f:S\rightarrow \mathbb{P}^1$ a $T^2$-fibration (not necessarily holomorphic, I have a special Langrangian fibration in mind). Assume there is a $k$-section, then a fiber ...
- 1
0
votes
0
answers
354
views
Linking L function dynamics with behavior close to s = 1 ?
A division, found on a sample set of semi-stable elliptic curves, calls for interpretation regarding the Birch and Swinnerton-Dyer conjecture and the dynamic behavior of the L functions involved.
...
0
votes
0
answers
229
views
Reduction of endomorphism ring of Non-CM elliptic curve
Let $E$ be an elliptic curve defined over a number field without complex multiplication and with ordinary reduction at a prime $p\in\mathbb{N}$. When is the reduction mod $p$ map a surjection on the ...
- 1
0
votes
0
answers
843
views
Cannonball problem using elliptic curves
I am basically trying to solve the cannonball problem using elliptic curves (see Ch 1 of Washington's book).
In other words I have to show that the only integer points on the "elliptic curve" $6y^2 = ...
- 562
0
votes
0
answers
352
views
Liftability in positive characteristic
What clsses of algebraic varieties over field of positive characteristic can be lift to $W_2(k)$?
- 85
0
votes
0
answers
524
views
DeRham cohomology
The Poincare lemma fails in positive characteristic, since pth powers vanish under differention. My question is : is there still some kind of resolution of the local system k by considering some ...
- 1
0
votes
0
answers
147
views
elementary question on ECDLP
If $\mathbb{F}_q$ is a finite field and the elliptic curve E is defined over finite field $\mathbb{F}_p$ such that ECDLP is hard in E($\mathbb{F}_p$), where $q, p$ are prime and $q \ll p$. Let T $\in ...
- 23
0
votes
0
answers
520
views
Motivation of proof of Riemann-Roch for elliptic curve and generalizations
Given a lattice $L \subseteq \mathbb{C}$, Alain Robert defines a theta function as a meromorphic function such that $\theta(z+\omega)=a(\omega) e^{\pi h(\omega)(z+\frac{\omega}{2})} \theta(z)$ for all ...
- 15.4k
-1
votes
1
answer
130
views
Is there an algorithm to find a linear dependence between points on elliptic curves?
Let $E$ be an elliptic curve over a finite field $\mathbb{F}_p$ of characteristic $p$. Let $P,Q\in E(\mathbb{F}_q)$, such that $Q=mP+n\tau(P)$, where $\tau$ is the p-th power of frobenious map and $m$ ...
- 369