CONSTRUCTING ALGEBRAIC CLOSURES KEITH CONRAD Let K be a field. We want to construct an algebraic closure of K, i.e., an algebraic extension of K which is algebraically closed. It will be built out of the quotient of a po

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Inequalities-1 Inequalities related to Lefschetz pencils and integrals of Chern classes Nicholas M. Katz and Rahul Pandharipande I n t r o d u c t i o n We work over an algebraically closed field k, in which a prime numb

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IMAGINARIES AND DEFINABLE TYPES IN ALGEBRAICALLY CLOSED VALUED FIELDS EHUD HRUSHOVSKI This manuscript is largely an exposition of material from [1], [2] and [3], regarding definable types in the model completion of the t

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• Algebra
• Abstract algebra
• Mathematics
• Field theory
• Algebraic geometry
• Valuation
• Sheaf
• Constructible universe
• Transcendental number
• Approximately finite-dimensional C*-algebra
• Differential forms on a Riemann surface

91 Documenta Math. Tame Class Field Theory for Singular Varieties over Algebraically Closed Fields

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• Abstract algebra
• Algebra
• Mathematics
• Algebraic geometry
• Cohomology theories
• Homological algebra
• Principal homogeneous space
• Cohomology
• Valuation
• Sheaf cohomology
• tale cohomology
• Torsor

A BABY STEP-GIANT STEP ROADMAP ALGORITHM FOR GENERAL ALGEBRAIC SETS ´ SCHOST S. BASU, M-F. ROY, M. SAFEY EL DIN, AND E. Abstract. Let R be a real closed field and D ⊂ R an ordered domain. We give an algorithm that tak

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• General topology
• Algebraic geometry
• Scheme theory
• Commutative algebra
• Algebraic varieties
• Algebraic curve
• Field extension
• Zariski topology
• Puiseux series
• Curve
• Quasi-algebraically closed field
• Algebraic extension

91 Documenta Math. Tame Class Field Theory for Singular Varieties over Algebraically Closed Fields

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• Algebraic geometry
• Cohomology theories
• Homological algebra
• Principal homogeneous space
• Cohomology
• Valuation
• Sheaf cohomology
• tale cohomology
• Torsor
• tale fundamental group
• Motivic cohomology
• Incomplete gamma function

REDUCTION RULES FOR LITTLEWOOD-RICHARDSON COEFFICIENTS MIKE ROTH A BSTRACT. Let G be a semisimple algebraic group over an algebraically-closed field of characteristic zero. In this note we show that every regular face of

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ON A RESULT OF ARTIN AISE JOHAN DE JONG Let k be an algebraically closed field of characteristic p > 0. Let t be a parameter and set S = Spec(k[[t]]). Let f : X → S be a smooth proper morphism with generic fibre Xη an

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• Algebra
• Homological algebra
• Algebraic geometry
• Crystalline cohomology
• Elementary class
• Structure
• Abstract algebra
• Model theory
• Mathematics

Conditions for Additional Roots from Maximal-Rank Minors of Macaulay Matrices Deepak Kapur1a , Manfred Minimairb a University of New Mexico, Department of Computer Science, Albuquerque, NM, USA

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• Determinants
• Matrix
• Emmy Noether
• Algebraically closed field
• Resultant
• Algebra
• Mathematics
• Polynomials

Algebra - Spring 2011 Daren Cheng Jesse Madnick Last updated: September 2013 Acknowledgments & Disclaimers Some of the solutions contained herein are my own, but many are not. I am indebted to Daren Cheng for sharing wit

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• Mathematics
• Polynomials
• Minimal polynomial
• Splitting field
• Algebraically closed field
• Finite field
• Field extension
• Algebraic integer
• Field
• Abstract algebra
• Algebra
• Field theory