Results 11 to 20 of about 36,541 (106)
Parity conjectures for elliptic curves over global fields of positive characteristic [PDF]
Compositio Mathematica, 2010 We prove the $p$-parity conjecture for elliptic curves over global fields of characteristic $p > 3$. We also present partial results on the $\ell$-parity conjecture for primes $\ell \neq p$.Comment: to be published in Compositio Mathematica. This version
Cassels +8 more
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On ring class eigenspaces of Mordell-Weil groups of elliptic curves over global function fields
Journal of Number Theory, 2008 If E is a non-isotrivial elliptic curve over a global function field F of odd characteristic we show that certain Mordell-Weil groups of E have 1-dimensional eigenspace relative to a fixed complex ring class character provided that the projection onto ...
Vigni, S.
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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 $1$.
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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
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International Mathematics Research Notices, 2023 Abstract Let $\mathbb{F}_{q}$ be a finite field whose characteristic is relatively prime to $2$ and $3$. Let $p$ be a prime number that is coprime to $q$. Let $E$ be an elliptic curve over the global function field $K = \mathbb{F}_{q}(t)$ such that $\textrm{Gal}(K(E[p])/K)$ contains the special linear group $\textrm{SL}_{2}(\mathbb{F}_{p}
Park, Sun Woo, Wang, Niudun
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Darmon points on elliptic curves over number fields of arbitrary signature [PDF]
, 2014 We present new constructions of complex and p-adic Darmon points on elliptic curves over base fields of arbitrary signature.
Guitart, Xavier +2 more
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First and second
Annales de l'Institut Fourier, 2018 In this paper, we show that the maximal divisible subgroup of groups K 1 and K 2 of an elliptic curve E over a function field is uniquely divisible. Further those K-groups modulo this uniquely divisible subgroup are explicitly computed. We also calculate the motivic cohomology groups of the minimal regular model of E, which is an elliptic surface ...
Kondo, Satoshi, Yasuda, Seidai
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Densities for Elliptic Curves over Global Function Fields
, 2023 Let $K$ be a global function field. We obtain a set of formulas for the densities of the Kodaira types and Tamagawa numbers of elliptic curves over a completion of $K$ that is independent of the field's characteristic. Furthermore, for a finite field $F$ and real numbers $s$ and $ε$ such that $s>1$ and $ε>0$, we prove that there exists a global ...
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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.
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Quadratic Chabauty for (bi)elliptic curves and Kim's conjecture
, 2020 We explore a number of problems related to the quadratic Chabauty method for determining integral points on hyperbolic curves. We remove the assumption of semistability in the description of the quadratic Chabauty sets $\mathcal{X}(\mathbb{Z}_p)_2 ...
Bianchi, Francesca
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