Algebraic function fields
at the University of Antwerp •
winter term 2024 •
by Ingo Blechschmidt
🎨 Exercises
💡 Syllabus
- The function field analogy
- Algebraic preliminaries
rings, integral domains, local rings, fields • polynomial rings
• localization • ideals, quotients by ideals, charts of ideals,
principal ideal domains • unique factorization domains • algebraic
closure
- Algebraic sets
affine space • zero loci and nonzero loci with examples and basic
properties • defining ideals and their reconstruction
- Affine varieties
irreducible algebraic sets • varieties in two-dimensional affine space
• Nullstellensatz corollaries • Noether normalization and dimension
• rings of germs • coordinate-free algebraic geometry
Rough transcript.
📖 References
💬 Contact
mail: iblech-antwerp@speicherleck.de
phone: +49 176 95110311 (also Telegram)