Results 51 to 60 of about 4,471 (200)
Mathematika, Volume 71, Issue 4, October 2025.Abstract Let E$E$ be an elliptic curve defined over Q${\mathbb {Q}}$, and let K$K$ be an imaginary quadratic field. Consider an odd prime p$p$ at which E$E$ has good supersingular reduction with ap(E)=0$a_p(E)=0$ and which is inert in K$K$. Under the assumption that the signed Selmer groups are cotorsion modules over the corresponding Iwasawa algebra ...
Erman Işik, Antonio Lei
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Endomorphism algebras of QM abelian surfaces
, 2013 We determine endomorphism algebras of abelian surfaces with quaternion multiplication.Comment: 14 pages.
Yu, Chia-Fu
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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
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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
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On supersingular elliptic curves and hypergeometric functions [PDF]
Involve, a Journal of Mathematics, 2012 The Legendre family of elliptic curves has the remarkable property that both its periods and its supersingular locus have descriptions in terms of the hypergeometric function [math] . In this work we study elliptic curves and elliptic integrals with respect to the hypergeometric functions [math] and [math] , and prove that the supersingular [math ...
openaire +2 more sources
Quantitative upper bounds related to an isogeny criterion for elliptic curves
Bulletin of the London Mathematical Society, Volume 56, Issue 8, Page 2661-2679, August 2024.Abstract For E1$E_1$ and E2$E_2$ elliptic curves defined over a number field K$K$, without complex multiplication, we consider the function FE1,E2(x)${\mathcal {F}}_{E_1, E_2}(x)$ counting nonzero prime ideals p$\mathfrak {p}$ of the ring of integers of K$K$, of good reduction for E1$E_1$ and E2$E_2$, of norm at most x$x$, and for which the Frobenius ...
Alina Carmen Cojocaru +2 more
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K3 surfaces of Kummer type in characteristic two
Bulletin of the London Mathematical Society, Volume 56, Issue 6, Page 1903-1919, June 2024.Abstract We discuss K3 surfaces in characteristic two that contain the Kummer configuration of smooth rational curves.
Igor V. Dolgachev
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The Endomorphism Rings of Supersingular Elliptic Curves over $\mathbb{F}_p$ and the Binary Quadratic Forms [PDF]
, 2022 Guanju Xiao +3 more
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Picard sheaves, local Brauer groups, and topological modular forms
Journal of Topology, Volume 17, Issue 2, June 2024.Abstract We develop tools to analyze and compare the Brauer groups of spectra such as periodic complex and real K$K$‐theory and topological modular forms, as well as the derived moduli stack of elliptic curves. In particular, we prove that the Brauer group of TMF$\mathrm{TMF}$ is isomorphic to the Brauer group of the derived moduli stack of elliptic ...
Benjamin Antieau +2 more
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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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