A Formalization of Complete Discrete Valuation Rings and Local Fields [PDF]
Certified Programs and Proofs, 2023 Local fields, and fields complete with respect to a discrete valuation, are essential objects in commutative algebra, with applications to number theory and algebraic geometry. We formalize in Lean the basic theory of discretely valued fields.
Mar'ia In'es de Frutos-Fern'andez +1 more
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Empowerment of Informal Settlements with Emphasis on Desirable Urban Governance Indicators (Case Study: Informal Settlements of Tabriz metropolis) [PDF]
برنامه ریزی فضایی, 2022 Today, one of the critical approaches to controlling and managing informal settlements is the approach of good urban governance. Good urban governance can be defined as the method and process of managing urban affairs with the constructive participation ...
Darioush Nowin +2 more
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Models of Abelian varieties over valued fields, using model theory [PDF]
Advances in Mathematics, 2023 Given an elliptic curve $E$ over a perfect defectless henselian valued field $(F,\mathrm{val})$ with perfect residue field $\textbf{k}_F$ and valuation ring $\mathcal{O}_F$, there exists an integral separated smooth group scheme $\mathcal{E}$ over ...
Yatir Halevi
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An inductive approach to representations of general linear groups over compact discrete valuation rings [PDF]
Advances in Mathematics, 2020 In his seminal Lecture Notes in Mathematics published in 1981, Andrey Zelevinsky introduced a new family of Hopf algebras which he called {\em PSH-algebras}. These algebras were designed to capture the representation theory of the symmetric groups and of
Tyrone Crisp, E. Meir, U. Onn
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Analyzing and Explaining the Relationship between University Field and the Legitimate Tastes of Tehran's Theater Audience [PDF]
جامعه شناسی کاربردی, 2019 Introduction The field of action of the spectator covers a broad range, from the simple act of buying a ticket to decoding and interpreting the performative text.
Farzan Sojoodi, Misagh Nemat Gorgani
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Ramification theory for degree p extensions of arbitrary valuation rings in mixed characteristic (0, p ) [PDF]
Journal of Algebra, 2017 We previously obtained a generalization and refinement of results about the ramification theory of Artin-Schreier extensions of discretely valued fields in characteristic $p$ with perfect residue fields to the case of fields with more general valuations ...
Vaidehee Thatte
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Valuation theory, generalized IFS attractors and fractals [PDF]
Archiv der Mathematik, 2018 Using valuation rings and valued fields as examples, we discuss in which ways the notions of “topological IFS attractor” and “fractal space” can be generalized to cover more general settings.
J. Dobrowolski, F. Kuhlmann
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Kummer Theory for Number Fields and the Reductions of Algebraic Numbers II
Uniform Distribution Theory, 2020 Let K be a number field, and let G be a finitely generated and torsion-free subgroup of K×. For almost all primes p of K, we consider the order of the cyclic group (G mod 𝔭), and ask whether this number lies in a given arithmetic progression.
Antonella Perucca, Pietro Sgobba
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Valuation theory of exponential Hardy fields II: Principal parts of germs in the Hardy field of o-minimal exponential expansions of the reals [PDF]
, 2012 We present a general structure theorem for the Hardy field of an o-minimal expansion of the reals by restricted analytic functions and an unrestricted exponential.
F. Kuhlmann, S. Kuhlmann
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Computing Tropical Varieties Over Fields with Valuation [PDF]
Foundations of Computational Mathematics, 2016 We show how the tropical variety of an ideal I⊴K[x1,…,xn]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength ...
Thomas Markwig, Yue Ren
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