Results 61 to 70 of about 42,992 (209)
Distribution of Mordell--Weil ranks of families of elliptic curves [PDF]
, 2016 We discuss the distribution of Mordell--Weil ranks of the family of elliptic curves $y^2=(x+\alpha f^2)(x+\beta b g^2)(x+\gamma h^2)$ where $f,g,h$ are coprime polynomials that parametrize the projective smooth conic $a^2+b^2=c^2$ and $\alpha,\beta ...
Naskręcki, Bartosz
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Equidistribution of Hecke points on the supersingular module
, 2012 For a fixed prime p, we consider the (finite) set of supersingular elliptic curves over $\bar{\mathbb{F}}$. Hecke operators act on this set. We compute the asymptotic frequence with which a given supersingular elliptic curve visits another under this ...
Menares, Ricardo
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WSEAS Transactions on Information Science and Applications, 2020 In this paper, an algebraic affine and projective curves of Edwards [3, 9] over the finite field Fpn . In the theory of Cryptosystems, Cryptology and Theoretical Computer Science it is well known that many modern cryptosystems [11] can be naturally ...
R. Skuratovskii, Mykola Bohdanenko
semanticscholar +1 more source
Dynamics on supersingular K3 surfaces [PDF]
, 2015 For any odd characteristic p=2 mod 3, we exhibit an explicit automorphism on the supersingular K3 surface of Artin invariant one which does not lift to any characteristic zero model.
Schuett, Matthias
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Rank parity for congruent supersingular elliptic curves [PDF]
Proceedings of the American Mathematical Society, 2017 A recent paper of Shekhar compares the ranks of elliptic curves E 1 E_1 and E 2 E_2 for which there is an isomorphism E 1 [ p ] ≃ E 2 [ p ] E_1[p] \simeq E_2[p]
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On the growth of $\mu $-invariant in Iwasawa theory of supersingular elliptic curves [PDF]
Acta Arithmetica, 2022 In this article, we provide a relation between the $ $-invariants of the dual plus and minus Selmer groups for supersingular elliptic curves when we ascend from the cyclotomic $\mathbb{Z}_p$-extension to a $\mathbb{Z}_p^2$-extension over an imaginary quadratic field.
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The 2‐divisibility of divisors on K3 surfaces in characteristic 2
Mathematische Nachrichten, Volume 298, Issue 6, Page 1964-1988, June 2025.Abstract We show that K3 surfaces in characteristic 2 can admit sets of n$n$ disjoint smooth rational curves whose sum is divisible by 2 in the Picard group, for each n=8,12,16,20$n=8,12,16,20$. More precisely, all values occur on supersingular K3 surfaces, with exceptions only at Artin invariants 1 and 10, while on K3 surfaces of finite height, only n=
Toshiyuki Katsura +2 more
wiley +1 more source
Oriented Supersingular Elliptic Curves and Eichler Orders
, 2023 Let $p>3$ be a prime and $E$ be a supersingular elliptic curve defined over $\mathbb{F}_{p^2}$. Let $c$ be a prime with $c < 3p/16$ and $G$ be a subgroup of $E[c]$ of order $c$. The pair $(E,G)$ is called a supersingular elliptic curve with level-$c$ structure, and the endomorphism ring $\text{End}(E,G)$ is isomorphic to an Eichler order with ...
Xiao, Guanju +2 more
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Arithmetic Satake compactifications and algebraic Drinfeld modular forms
Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.Abstract In this article, we construct the arithmetic Satake compactification of the Drinfeld moduli schemes of arbitrary rank over the ring of integers of any global function field away from the level structure, and show that the universal family extends uniquely to a generalized Drinfeld module over the compactification.
Urs Hartl, Chia‐Fu Yu
wiley +1 more source
Supersingular K3 Surfaces are Unirational
, 2014 We show that supersingular K3 surfaces in characteristic $p\geq5$ are related by purely inseparable isogenies. This implies that they are unirational, which proves conjectures of Artin, Rudakov, Shafarevich, and Shioda.
Liedtke, Christian
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