We introduce a class of parameter-dependent q-series arising from the moduli of certain pencils of elliptic curves and rank 19 lattice polarized K3 surfaces. These series serve to ‘link’ the various Hauptmoduln which arise as modular mirror maps (as characterized in [C. F. Doran, in The arithmetic and geometry of algebraic cycles (Banff, AB, 1998), CRM Proc. Lect. Notes 24, 257–281 (2000; Zbl 0972.14033); Commun. Math. Phys. 212, 625–647 (2000; Zbl 1047.11043)]), and can in principle be computed from the functional invariants of the pencils. Each corresponds to an algebraic solution to an isomonodromic deformation equation which parametrizes the Hurwitz space for those invariants. The discussion is made more concrete in the context of the Painlevé VI equation.
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June 2013 · Journal of Logic and Computation
A famous result, conjectured by Gödel in 1932 and proved by McKinsey and Tarski in 1948, says that ϕ ϕ is a theorem of intuitionistic propositional logic IPC iff its Gödel-translation ϕ ′ ϕ′ is a theorem of modal logic S4. In this article, we extend an intuitionistic version of modal logic S1 + SP, introduced in
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algebras with a (non-normal) modal operator. View full-text October 2009 · Communications in Algebra
In this article, I will prove that assuming Schanuel's conjecture, an exponential polynomial with algebraic coefficients can have only finitely many algebraic roots. Furthermore, this proof demonstrates that there are no unexpected algebraic roots of any such exponential polynomial. This implies a special case of Shapiro's conjecture: if p(x) and q(x) are two exponential polynomials with
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We investigate, in this article, a generalization of the Riemann–Roch theorem for graphs of Baker and Norine, with a view
toward identifying new objects for which a two-variable zeta-function can be defined. To a lattice Λ of rank n−1 in and perpendicular to a positive integer vector R, we define the notions of g-number and of canonical vector, in analogy with the notions of genus and canonical
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existence theorem using methods from arithmetic geometry. We show that a two-variable zeta-function can be defined when a
canonical vector exists. Read more Article
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December 2011 · Information (Switzerland)
Information is usually related to knowledge. However, the recent development of information theory demonstrated that information is a much broader concept, being actually present in and virtually related to everything. As a result, many unknown types and kinds of information have been discovered. Nevertheless, information that acts on knowledge, bringing new and updating existing knowledge, is of
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In this paper we introduce the notion of global equivariant hom-Lie algebra. This is a Lie algebra-like structure associated with twisted derivations. We prove several results on the structure of modules of twisted derivations and how they form global equivariant hom-Lie algebras. Particular emphasis is put on examples and results in arithmetic geometry.
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We define a superspace over a ring R as a functor on a subcategory of the category of supercommutative R-algebras. As an application the notion of a p-adic superspace is introduced and used to give a transparent construction of the Frobenius map on p-adic cohomology of a smooth projective variety over Zp (the ring of p-adic integers).
Read more November 2009 · Annals of Pure and Applied Logic
Glivenko-type theorems for substructural logics (over FL) are comprehensively studied in the paper [N. Galatos, H. Ono, Glivenko theorems for substructural logics over FL, Journal of Symbolic Logic 71 (2006) 1353-1384]. Arguments used there are fully algebraic, and based on the fact that all substructural logics are algebraizable (see [N. Galatos, H. Ono, Algebraization, parametrized local
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July 2016 · Compositio Mathematica
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This thesis explores a variety of topics in two-dimensional arithmetic geometry, including the further development of I. Fesenko's adelic analysis and its relations with ramification theory, model-theoretic integration on valued fields, and Grothendieck duality on arithmetic surfaces.
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It is explained how the motivic integration theory of E. Hrushovski and D. Kazhdan can be modified to provide a model-theoretic approach to integration on two-dimensional local fields. The possible unification of this work with A. Abbes and T. Saito's ramification theory is explored.
Relationships between Fubini's theorem, ramification theory, and Riemann-Hurwitz formulae are established in the setting of curves and surfaces over an algebraically closed field.
A theory of residues for arithmetic surfaces is developed, and the reciprocity law around a point is established. The residue maps are used to explicitly construct the dualising sheaf of the surface. Read more Last Updated: 04 Jul 2022
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