TL;DR
This paper provides a comprehensive analysis of the concepts of irreducibility and integrity in schemes, exploring their global, local, and pointwise variants with illustrative examples for educational purposes.
Contribution
It systematically examines the relationships between different notions of irreducibility and integrity in schemes, including examples and counterexamples, for the first time in a unified manner.
Findings
Clarified the connections between global, local, and pointwise irreducibility.
Provided new examples and counterexamples illustrating these concepts.
Enhanced understanding of scheme properties for learners.
Abstract
This is a comprehensive study of the relations between the global, local and pointwise variants of irreducibility and integrity of schemes, including examples and counterexamples, and aimed especially at learners of algebraic geometry.
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