Results 11 to 20 of about 2,867,834 (292)
Rational and singular points of a family of curves
Results in Applied MathematicsThis paper explores the properties of a family of absolutely irreducible projective plane curves, denoted Ca,b, which are defined over a finite field Fm of characteristic 2.
M.C. Rodríguez-Palánquex
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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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Some aspects of rational points and rational curves [PDF]
, 2023 Various methods have been used to construct rational points and rational curves on rationally connected algebraic varieties. We survey recent advances in two of them, the descent and the fibration method, in a number-theoretical context (rational points over number fields) and in an algebro-geometric one (rational curves on real varieties), and discuss
Wittenberg, Olivier
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Rational points on curves [PDF]
Journal de théorie des nombres de Bordeaux, 2011 This is an extended version of an invited lecture I gave at the Journées Arithmétiques in St. Étienne in July 2009. We discuss the state of the art regarding the problem of finding the set of rational points on a (smooth projective) geometrically integral curve C
Michael Stoll, Stoll, Michael
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Rational points on a certain genus 2 curve
Comptes Rendus. Mathématique, 2023 We give a correct proof to the fact that all rational points on the curve \[ y^2=(x^2+1)(x^2+3)(x^2+7) \] are $\pm \infty $ and $(\pm 1,\,\pm 8)$. This corrects previous works of Cohen [3] and Duquesne [4, 5].
Nguyen, Xuan Tho
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Rational Singularities and Rational Points [PDF]
Pure and Applied Mathematics Quarterly, 2008 If $X$ is a projective, geometrically irreducible variety defined over a finite field $\F_q$, such that it is smooth and its Chow group of 0-cycles fulfills base change, i.e. $CH_0(X\times_{\F_q}\bar{\F_q(X)})=\Q$, then the second author's theorem asserts that its number of rational points satisfies $|X(\F_q)| \equiv 1$ modulo $q$. If $X$ is not smooth,
Blickle, Manuel, Esnault, Hélène
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On rational points in CFT moduli spaces
Journal of High Energy Physics, 2021 Motivated by the search for rational points in moduli spaces of two-dimensional conformal field theories, we investigate how points with enhanced symmetry algebras are distributed there.
Nathan Benjamin +3 more
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Families of polynomials of every degree with no rational preperiodic points
Comptes Rendus. Mathématique, 2021 Let $K$ be a number field. Given a polynomial $f(x)\in K[x]$ of degree $d\ge 2$, it is conjectured that the number of preperiodic points of $f$ is bounded by a uniform bound that depends only on $d$ and $[K:\mathbb{Q}]$.
Sadek, Mohammad
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Primitive Points in Rational Polygons [PDF]
Canadian Mathematical Bulletin, 2020 AbstractLet ${\mathcal{A}}$ be a star-shaped polygon in the plane, with rational vertices, containing the origin. The number of primitive lattice points in the dilate $t{\mathcal{A}}$ is asymptotically $\frac{6}{\unicode[STIX]{x1D70B}^{2}}\text{Area}(t{\mathcal{A}})$ as $t\rightarrow \infty$. We show that the error term is both $\unicode[STIX]{x1D6FA}_{
Bárány, I +3 more
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Heights on stacks and a generalized Batyrev–Manin–Malle conjecture
Forum of Mathematics, Sigma, 2023 We define a notion of height for rational points with respect to a vector bundle on a proper algebraic stack with finite diagonal over a global field, which generalizes the usual notion for rational points on projective varieties.
Jordan S. Ellenberg +2 more
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