Elementary Algebraic Geometry
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In this first part, we give a quick overview of some of the foundational material of elementary algebraic geometry needed for a study of motivic homotopy theory. All of this material is well-known and excellently discussed in numerous texts; our goal is to collect the main facts to give the reader a convenient first introduction and quick reference. For this reason, many of the proofs will be only sketched or completely omitted. For further details, we suggest the reader take a look at , ,  for the commutative algebra and ,  or  for the algebraic geometry; for a more analytic point of view, we suggest .
KeywordsPrime Ideal Commutative Ring Noetherian Ring Ring Homomorphism Smooth Point
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