Solutions to arithmetic differential equations in algebraically closed fields
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In this paper, the authors introduce a rescaling process which identifies a class of δ-functions called totally overconvergent, which extend all the way to the algebraic closure of ring of integers of the maximally unramified extension of Q p. Applications built on these functions allow one to remove boundedness assumptions on ramification.About:
This article is published in Advances in Mathematics.The article was published on 2020-12-02 and is currently open access. It has received 3 citations till now. The article focuses on the topics: Algebraic closure & Isogeny.read more
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Reversible Thinking of Fifth Graders: Focus on Linier Equations
TL;DR: This paper explored the reversible thinking of fifth grade elementary school students on linear equations and found that the most diverse approach was selected to be explored more deeply in reversible thinking, among others, moving the elements of the initial equation builder, determining the unknown factors.
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Purely arithmetic PDE's over a p-adic field I: delta-characters and delta-modular forms
TL;DR: In this article, a formalism of arithmetic partial differential equations (PDEs) is developed in which one considers several arithmetic differentiations at one fixed prime, and solutions can be defined in algebraically closed p-adic fields.
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Canonical Witt formal scheme extensions and p-torsion groups
TL;DR: In this article , the n th arithmetic jet space of the p -torsion subgroup attached to a smooth commutative formal group scheme was studied, and it was shown that it fits in the middle of a canonical short exact sequence between a power of the formal scheme of Witt vectors of length n and the p-torsions subgroup.
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P-ADIC Properties of Modular Schemes and Modular Forms
TL;DR: In this article, a modular form of weight k and level n becomes a section of a certain line bundle, and the reduction modulo p of identical relations which hold over the line bundle is obtained.
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Formal Groups and Applications
TL;DR: This book is a comprehensive treatment of the theory of formal groups and its numerous applications in several areas of mathematics, including very important applications in algebraic topology, number theory, and algebraic geometry.
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