Results 1 to 10 of about 667 (60)
The most efficient indifferentiable hashing to elliptic curves of j-invariant 1728
Journal of Mathematical Cryptology, 2022 This article makes an important contribution to solving the long-standing problem of whether all elliptic curves can be equipped with a hash function (indifferentiable from a random oracle) whose running time amounts to one exponentiation in the basic ...
Koshelev Dmitrii
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Quartic and Quintic Hypersurfaces with Dense Rational Points
Forum of Mathematics, Sigma, 2023 Let $X_4\subset \mathbb {P}^{n+1}$ be a quartic hypersurface of dimension $n\geq 4$ over an infinite field k. We show that if either $X_4$ contains a linear subspace $\Lambda $ of dimension $h\geq \max \{2,\dim (\Lambda ...
Alex Massarenti
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Point counting for foliations over number fields
Forum of Mathematics, Pi, 2022 Let${\mathbb M}$ be an affine variety equipped with a foliation, both defined over a number field ${\mathbb K}$. For an algebraic $V\subset {\mathbb M}$ over ${\mathbb K}$, write $\delta _{V}$ for the maximum of the degree and log-height of V.
Gal Binyamini
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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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Hensel minimality II: Mixed characteristic and a diophantine application
Forum of Mathematics, Sigma, 2023 In this paper, together with the preceding Part I [10], we develop a framework for tame geometry on Henselian valued fields of characteristic zero, called Hensel minimality. It adds to [10] the treatment of the mixed characteristic case.
Raf Cluckers +3 more
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Nonspecial varieties and generalised Lang–Vojta conjectures
Forum of Mathematics, Sigma, 2021 We construct a family of fibred threefolds $X_m \to (S , \Delta )$ such that $X_m$ has no étale cover that dominates a variety of general type but it dominates the orbifold $(S,\Delta )$ of general type. Following Campana, the threefolds $X_m$ are called
Erwan Rousseau +2 more
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A complete characterization of Galois subfields of the generalized Giulietti--Korchm\'aros function field [PDF]
, 2016 We give a complete characterization of all Galois subfields of the generalized Giulietti--Korchm\'aros function fields $\mathcal C_n / \fqn$ for $n\ge 5$.
Anbar, Nurdagül +2 more
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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
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A unique pair of triangles [PDF]
, 2018 A rational triangle is a triangle with sides of rational lengths. In this short note, we prove that there exists a unique pair of a rational right triangle and a rational isosceles triangle which have the same perimeter and the same area.
Hirakawa, Yoshinosuke, Matsumura, Hideki
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Counting rational points on smooth cubic surfaces [PDF]
, 2016 We prove that any smooth cubic surface defined over any number field satisfies the lower bound predicted by Manin's conjecture possibly after an extension of small degree.Comment: 11 pages, minor ...
Frei, Christopher, Sofos, Efthymios
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