Results 1 to 10 of about 510 (96)
The conjectures of Artin-Tate and Birch-Swinnerton-Dyer [PDF]
Épijournal de Géométrie Algébrique, 2022 We provide two proofs that the conjecture of Artin-Tate for a fibered surface is equivalent to the conjecture of Birch-Swinnerton-Dyer for the Jacobian of the generic fibre.
S. Lichtenbaum +2 more
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An extension to the planar Markus–Yamabe Jacobian conjecture
Electronic Journal of Qualitative Theory of Differential Equations, 2021 We extend the planar Markus–Yamabe Jacobian conjecture to differential systems having Jacobian matrix with eigenvalues with negative or zero real parts.
Marco Sabatini
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Attacking Jacobian Problem Using Resultant Theory
مجلة بغداد للعلوم, 2022 This paper introduces a relation between resultant and the Jacobian determinant by generalizing Sakkalis theorem from two polynomials in two variables to the case of (n) polynomials in (n) variables. This leads us to study the results of the type:
Alaa Jony, Shawki Al-Rashed
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Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces
Comptes Rendus. Mathématique, 2022 Let $X$ be one of the $28$ Atkin–Lehner quotients of a curve $X_0(N)$ such that $X$ has genus $2$ and its Jacobian variety $J$ is absolutely simple. We show that the Shafarevich–Tate group $\Sha (J/\mathbb{Q})$ is trivial.
Keller, Timo, Stoll, Michael
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JACOBIAN CONJECTURE, TWO-DIMENSIONAL CASE
Проблемы анализа, 2016 The Jacobian Conjecture was first formulated by O. Keller in 1939. In the modern form it supposes injectivity of the polynomial mapping f: R^n → R^n (C^n → C^n) provided that jacobian J_f ≡ const ≠ 0.
V. V. Starkov
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Polynomial Automorphisms, Deformation Quantization and Some Applications on Noncommutative Algebras
Mathematics, 2022 This paper surveys results concerning the quantization approach to the Jacobian Conjecture and related topics on noncommutative algebras. We start with a brief review of the paper and its motivations.
Wenchao Zhang +5 more
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THE JACOBIAN CONJECTURE: STRUCTURE OF KELLER MAPPINGS
Проблемы анализа, 2019 The Jacobian conjecture was first formulated by O. N. Keller in 1939. In the modern form it supposes injectivity of the polynomial mapping f : R n → R n (C n → C n ) under the assumption that Jf ≡ const 6= 0.
V. V. Starkov
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STRUCTURE OF KELLER MAPPINGS, TWO-DIMENSIONAL CASE
Проблемы анализа, 2017 A Keller map is a polynomial mapping ƒ : Rⁿ → Rⁿ (or Cⁿ → Cⁿ) with the Jacobian J_ƒ ≡ const ≠ 0. The Jacobian conjecture was first formulated by O. N. Keller in 1939. In the modern form it supposes injectivity of a Keller map. Earlier, in the case n = 2,
V. V. Starkov
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Analytic Automorphisms and Transitivity of Analytic Mappings
Mathematics, 2020 In this paper, we investigate analytic automorphisms of complex topological vector spaces and their applications to linear and nonlinear transitive operators.
Zoriana Novosad, Andriy Zagorodnyuk
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A Survey of Research on Square-Free and Radical Factorizations:from Jacobian-Type Conditions to Ideals in Noncommutative Rings [PDF]
Military Technology and ScienceThis article presents a survey of research on square-free and radical factorizations in rings and monoids, both in the commutativeand noncommutative settings.
Łukasz Matysiak
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