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Commutative Algebra I

Craig Huneke
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TLDR
A compilation of two sets of notes at the University of Kansas was published in the Spring of 2002 by?? and the other in the spring of 2007 by Branden Stone.
Abstract
1 A compilation of two sets of notes at the University of Kansas; one in the Spring of 2002 by ?? and the other in the Spring of 2007 by Branden Stone. These notes have been typed

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On the birational anabelian program initiated by Bogomolov I

TL;DR: In this article, the authors complete the Bogomolov program in the case k is an algebraic closure of a finite field, where l is any prime number ≠char(k).
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Algebras with a negation map

TL;DR: This article studied algebraic structures with negation maps in the context of universal algebra, showing how these unify the more viable (super)tropical versions, as well as hypergroup theory and fuzzy rings, thereby "explaining" similarities in their theories.
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Computing differential characteristic sets by change of ordering

TL;DR: An algorithm for converting a characteristic set of a prime differential ideal from one ranking into another is described and permitted to solve formerly unsolved problems.
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A skeleton key to Abhyankar's proof of embedded resolution of characteristic P surfaces

TL;DR: Abhyankar as mentioned in this paper analyzes and simplifies the proof of embedded resolution of surface singularities in positive characteristic by combining the results in the papers [2], [4], [5], [6] and the first two chapters of the book [7].
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The moduli stack of $G$-bundles

TL;DR: The geometric properties of the moduli stack of a moduli bundle are studied in this article, where it is shown that it is an algebraic stack locally of finite presentation over a base field and a flat, finitely presented, projective morphism of schemes.
References
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Book

Introduction to Commutative Algebra

TL;DR: It is shown here how the Noetherian Rings and Dedekind Domains can be transformed into rings and Modules of Fractions using the following structures: