This second volume completes the foundational journey through modern algebraic geometry, building upon Volume I’s treatment of field theory and Dedekind domains. Designed for researchers and graduate students, this text:
Core Features:
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Arithmetic-Algebraic Bridge: Systematically connects ring theory to algebraic geometry
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Place Theory: Detailed treatment of valuations and places with geometric applications
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Power Series Methods: Classical results on polynomial/power series rings for variety analysis
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Local Algebra: Comprehensive chapter on local rings as basis for singularity studies
Pedagogical Strengths:
✓ 50+ exercises linking theory to computational practice
✓ Self-contained proofs for all major theorems
✓ Historical notes on Zariski’s contributions
✓ Appendixes with Krull dimension tables
Unique Value Proposition:
While Volume I established ideal-theoretic foundations, this volume:
• Develops tools for arithmetic geometry (Weil conjectures)
• Provides algebraic preparation for scheme theory
• Clarifies local-global principles in variety theory
