Results 11 to 20 of about 966 (79)
Transactions of the London Mathematical Society, 2019 Recently, there has been much interest in studying the torsion subgroups of elliptic curves base‐extended to infinite extensions of Q. In this paper, given a finite group G, we study what happens with the torsion of an elliptic curve E over Q when ...
Harris B. Daniels +2 more
doaj +2 more sources
Non‐vanishing theorems for central L‐values of some elliptic curves with complex multiplication
Proceedings of the London Mathematical Society, Volume 121, Issue 6, Page 1531-1578, December 2020., 2020 Abstract The paper uses Iwasawa theory at the prime p=2 to prove non‐vanishing theorems for the value at s=1 of the complex L‐series of certain quadratic twists of the Gross family of elliptic curves with complex multiplication by the field K=Q(−q), where q is any prime ≡7mod8.
John Coates, Yongxiong Li
wiley +1 more source
Models of hyperelliptic curves with tame potentially semistable reduction
Transactions of the London Mathematical Society, Volume 7, Issue 1, Page 49-95, December 2020., 2020 Abstract Let C be a hyperelliptic curve y2=f(x) over a discretely valued field K. The p‐adic distances between the roots of f(x) can be described by a completely combinatorial object known as the cluster picture. We show that the cluster picture of C, along with the leading coefficient of f and the action of Gal(K¯/K) on the roots of f, completely ...
Omri Faraggi, Sarah Nowell
wiley +1 more source
Conductor and discriminant of Picard curves
Journal of the London Mathematical Society, Volume 102, Issue 1, Page 368-404, August 2020., 2020 Abstract We describe normal forms and minimal models of Picard curves, discussing various arithmetic aspects of these. We determine all so‐called special Picard curves over Q with good reduction outside 2 and 3, and use this to determine the smallest possible conductor a special Picard curve may have.
Irene I. Bouw +3 more
wiley +1 more source
Torsion subgroups of rational Mordell curves over some families of number fields
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 Mordell curves over a number field K are elliptic curves of the form y2 = x3 + c, where c ∈ K \ {0}. Let p ≥ 5 be a prime number, K a number field such that [K : ℚ] ∈ {2p, 3p}.
Gužvić Tomislav, Roy Bidisha
doaj +1 more source
L‐equivalence for degree five elliptic curves, elliptic fibrations and K3 surfaces
Bulletin of the London Mathematical Society, Volume 52, Issue 2, Page 395-409, April 2020., 2020 Abstract We construct non‐trivial L‐equivalence between curves of genus one and degree five, and between elliptic surfaces of multisection index five. These results give the first examples of L‐equivalence for curves (necessarily over non‐algebraically closed fields) and provide a new bit of evidence for the conjectural relationship between L ...
Evgeny Shinder, Ziyu Zhang
wiley +1 more source
Base change for Elliptic Curves over Real Quadratic Fields [PDF]
, 2014 Let E be an elliptic curve over a real quadratic field K and F/K a totally real finite Galois extension. We prove that E/F is modular.Comment: added a short proof of Proposition 2.1 and a few more small changes to improve ...
Dieulefait, Luis, Freitas, Nuno
core +4 more sources
Toroidal and Annular Dehn Fillings [PDF]
, 1997 Suppose that M is a hyperbolic 3‐manifold which admits two Dehn fillings M(r1) and M(r2) such that M(r1) contains an essential annulus, and M(r2) contains an essential torus. It is known that Δ = Δ (r1, r2) ⩽ 5.
C. Gordon, Ying‐Qing Wu
semanticscholar +1 more source
Torsion of elliptic curves over quadratic cyclotomic fields [PDF]
, 2010 In this paper we study the possible torsions of elliptic curves over $\mathbb Q(i)$ and $\mathbb Q(\sqrt {-3})$.Comment: 9 pages, to appear in Math. J.
Najman, Filip
core +3 more sources
GOLDFELD’S CONJECTURE AND CONGRUENCES BETWEEN HEEGNER POINTS
Forum of Mathematics, Sigma, 2019 Given an elliptic curve $E$ over $\mathbb{Q}$, a celebrated conjecture of Goldfeld asserts that a positive proportion of its quadratic twists should have analytic rank 0 (respectively 1).
DANIEL KRIZ, CHAO LI
doaj +1 more source