Results 1 to 10 of about 3,799,599 (344)
Lattices and Rational Points [PDF]
Mathematics, 2017 In this article, we show how to use the first and second Minkowski Theorems and some Diophantine geometry to bound explicitly the height of the points of rank N - 1 on transverse curves in E N , where E is an elliptic curve without Complex
Evelina Viada
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Sieving rational points on varieties [PDF]
Transactions of the American Mathematical Society, 2018 An upper bound sieve for rational points on suitable varieties is developed, together with applications to counting rational points in thin sets, to local solubility in families, and to the notion of “friable” rational points with respect to divisors. In the special case of quadrics, sharper estimates are obtained by developing a version of the Selberg
Browning, Tim, Loughran, Daniel
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Translates of rational points along expanding closed horocycles on the modular surface. [PDF]
Math Ann, 2022 We study the limiting distribution of the rational points under a horizontal translation along a sequence of expanding closed horocycles on the modular surface.
Burrin C, Shapira U, Yu S.
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Supersolvable descent for rational points [PDF]
Algebra & Number Theory, 2022 We construct an analogue of the classical descent theory of Colliot-Th\'el\`ene and Sansuc in which algebraic tori are replaced with finite supersolvable groups. As an application, we show that rational points are dense in the Brauer-Manin set for smooth
Yonatan Harpaz, Olivier Wittenberg
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Density of rational points near/on compact manifolds with certain curvature conditions [PDF]
Advances in Mathematics, 2021 In this article we establish an asymptotic formula for the number of rational points, with bounded denominators, within a given distance to a compact submanifold M ofR with a certain curvature condition.
D. Schindler, S. Yamagishi
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Quartic surfaces, their bitangents and rational points [PDF]
Épijournal de Géométrie Algébrique, 2023 Let X be a smooth quartic surface not containing lines, defined over a number field K. We prove that there are only finitely many bitangents to X which are defined over K.
Pietro Corvaja, Francesco Zucconi
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Which rational double points occur on del Pezzo surfaces? [PDF]
Épijournal de Géométrie Algébrique, 2021 We determine all configurations of rational double points that occur on RDP del Pezzo surfaces of arbitrary degree and Picard rank over an algebraically closed field $k$ of arbitrary characteristic ${\rm char}(k)=p \geq 0$, generalizing classical work of
Claudia Stadlmayr
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Counting rational points on projective varieties
Proceedings of the London Mathematical Society, 2023 We develop a global version of Heath‐Brown's p‐adic determinant method to study the asymptotic behaviour of the number N(W; B) of rational points of height at most B on certain subvarieties W of Pn defined over Q.
P. Salberger
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On homogeneous spaces with finite anti-solvable stabilizers
Comptes Rendus. Mathématique, 2022 We say that a group is anti-solvable if all of its composition factors are non-abelian. We consider a particular family of anti-solvable finite groups containing the simple alternating groups for $n\ne 6$ and all 26 sporadic simple groups. We prove that,
Lucchini Arteche, Giancarlo
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On the distribution of rational points on ramified covers of abelian varieties [PDF]
Compositio Mathematica, 2020 We prove new results on the distribution of rational points on ramified covers of abelian varieties over finitely generated fields $k$ of characteristic zero.
P. Corvaja +4 more
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