Results 11 to 20 of about 51 (51)
Pseudo-split fibres and arithmetic surjectivity
, 2020 Let f : X ! Y be a dominant morphism of smooth, proper and geometrically integral varieties over a number field k, with geometrically integral generic fibre. We give a necessary and sufficient geometric criterion for the induced map X(kv) !
Smeets, A. +7 more
core +1 more source
How to generate all integral triangles containing a given angle
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 8, Page 569-572, 2000., 2000 We present an elementary prescription based on the rational secant method for generating all the integral triangles containing a given angle of rational cosine. This is a direct generalization of the ancient problem of finding all the Pythagorean triples. As an example, we discuss a specific equation studied by Diophantus of Alexandria, which turns out
Nelson Petulante, Ifeoma Kaja
wiley +1 more source
$E_{6}$ AND THE ARITHMETIC OF A FAMILY OF NON-HYPERELLIPTIC CURVES OF GENUS 3
Forum of Mathematics, Pi, 2015 We study the arithmetic of a family of non-hyperelliptic curves of genus 3 over the field $\mathbb{Q}$ of rational numbers. These curves are the nearby fibers of the semi-universal deformation of a simple singularity of type $E_{6}$. We show that average
JACK A. THORNE
doaj +1 more source
NON-ARCHIMEDEAN YOMDIN–GROMOV PARAMETRIZATIONS AND POINTS OF BOUNDED HEIGHT
Forum of Mathematics, Pi, 2015 We prove an analog of the Yomdin–Gromov lemma for $p$-adic definable sets and more broadly in a non-Archimedean definable context. This analog keeps track of piecewise approximation by Taylor polynomials, a nontrivial aspect in the totally disconnected ...
RAF CLUCKERS +2 more
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An elliptic Diophantine equation from the study of partitions
, 2019 We present the elliptic equation X3 + 2 = Y 2 as the first in a sequence of Diophantine equations arising from some new results in the theory of partitions of multisets with equal sums.
ANDRICA, Dorin, ȚURCAȘ, George C.
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Complete verification of strong BSD for many modular abelian surfaces over ${\mathbf {Q}}$
Forum of Mathematics, SigmaWe develop the theory and algorithms necessary to be able to verify the strong Birch–Swinnerton-Dyer Conjecture for absolutely simple modular abelian varieties over ${\mathbf {Q}}$ . We apply our methods to all 28 Atkin–Lehner quotients of $X_0(
Timo Keller, Michael Stoll
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Rational torsion points on abelian surfaces with quaternionic multiplication
Forum of Mathematics, SigmaLet A be an abelian surface over ${\mathbb {Q}}$ whose geometric endomorphism ring is a maximal order in a non-split quaternion algebra. Inspired by Mazur’s theorem for elliptic curves, we show that the torsion subgroup of $A({\mathbb {Q}})$
Jef Laga +3 more
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Rank jumps and multisections of elliptic fibrations on K3 surfaces
Forum of Mathematics, SigmaWe consider the countably many families $\mathcal {L}_d$ , $d\in \mathbb {N}_{\geq 2}$ , of K3 surfaces admitting an elliptic fibration with positive Mordell–Weil rank. We prove that the elliptic fibrations on the very general member of these
Alice Garbagnati, Cecília Salgado
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The genus of curves over finite fields with many rational points, [PDF]
, 1996 . We prove the following result which was conjectured by Stichtenoth and Xing: let g be the genus of a projective, non-singular, geometrically irreducible, algebraic curve defined over the finite field with q 2 elements whose number of rational points ...
Rainer Fuhrmann, Fernando Torres
core
The Manin–Peyre conjecture for smooth spherical Fano varieties of semisimple rank one
Forum of Mathematics, SigmaThe Manin–Peyre conjecture is established for a class of smooth spherical Fano varieties of semisimple rank one. This includes all smooth spherical Fano threefolds of type T as well as some higher-dimensional smooth spherical Fano varieties.
Valentin Blomer +3 more
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