Results 1 to 10 of about 865 (232)
Structure of Tate–Shafarevich groups of elliptic curves over global function fields [PDF]
Kyoto Journal of Mathematics, 2015 The structure of the Tate-Shafarevich groups of a class of elliptic curves over global function fields is determined. These are known to be finite abelian groups from the monograph [1] and hence they are direct sums of finite cyclic groups where the orders of these cyclic components are invariants of the Tate-Shafarevich group.
Brown, Martin L.
exaly +6 more sources
On ring class eigenspaces of Mordell–Weil groups of elliptic curves over global function fields
Journal of Number Theory, 2008 20 pages, to appear in J.
Stefano Vigni
exaly +7 more sources
Parity conjectures for elliptic curves over global fields of positive characteristic [PDF]
Compositio Mathematica, 2011 Abstract We prove the p -parity conjecture for elliptic curves over global fields of characteristic p >3. We also present partial results on the ℓ -parity conjecture for primes
Trihan, Fabien, Wuthrich, Christian
openaire +3 more sources
Most elliptic curves over global function fields are torsion free [PDF]
Acta Arithmetica, 2022 Given an elliptic curve $E$ over a global function field $K$, the Galois action on the $n$-torsion points of $E$ gives rise to a mod-n Galois representation $ρ_{E,n}$. For $K$ satisfying some mild conditions, we show that the set of $E$ for which $ρ_{E,n}$ is as large as possible for all $n$, has density $1$.
Phillips, Tristan
openaire +3 more sources
, 2022 Fix a prime number $p$. Let $\mathbb{F}_q$ be a finite field of characteristic coprime to 2, 3, and $p$, which also contains the primitive $p$-th root of unity $μ_p$. Based on the works by Swinnerton-Dyer and Klagsbrun, Mazur, and Rubin, we prove that the probability distribution of the sizes of prime Selmer groups over a family of cyclic prime twists ...
Park, Sun Woo
core +5 more sources
Local-global principle for isogenies of elliptic curves over quadratic fields
In this paper, we prove that the local-global principle of 11-isogenies for elliptic curves over quadratic fields does not fail. This gives a positive answer to a conjecture by Banwait and Cremona. The proof is based on the determination of the set of quadratic points on the modular curve XD10(11).
Gajović, S. ; https://orcid.org/0000-0003-3846-5199 +2 more
openaire +3 more sources
Heegner Points and the Rank of Elliptic Curves over Large Extensions of Global Fields [PDF]
Canadian Journal of Mathematics, 2008 AbstractLetkbe a global field,a separable closure ofk, andGkthe absolute Galois groupofoverk. For everyσ ∈ Gk, letbe the fixed subfield ofunderσ. LetE/kbe an elliptic curve overk. It is known that the Mordell–Weil grouphas infinite rank. We present a new proof of this fact in the following two cases.
Breuer, Florian, Im, Bo-Hae
openaire +2 more sources
Darmon points on elliptic curves over number fields of arbitrary signature [PDF]
, 2014 We present new constructions of complex and pp-adic Darmon points on elliptic curves over base fields of arbitrary signature.
Guitart, X. +8 more
core +3 more sources
Trace zero varieties in cryptography : optimal representation and index calculus [PDF]
, 2014 The trace zero variety associated to an elliptic or hyperelliptic curve is an abelian variety defined over a finite field F_q. Its F_q-rational points yield a finite group, the trace zero subgroup of the degree zero Picard group of the original curve ...
Massierer, Maike
core +1 more source
On 7-division fields of CM elliptic curves [PDF]
, 2023 Let e be a CM elliptic curve defined over a number field K, with Weiestrass form y^2 = x^3 + bx or y^2 = x^3 + c. For every positive integer m, we denote by e[m] the m-torsion subgroup of E and by K-m ..= K (e[m]) the m-th division field, i.e.
Paladino Laura +3 more
core +1 more source