Algebraic function fields


at the University of Antwerp • winter term 2024 • by Ingo Blechschmidt

🎨 Exercises

💡 Syllabus

  1. The function field analogy
  2. 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
  3. Algebraic sets
    affine space • zero loci and nonzero loci with examples and basic properties • defining ideals and their reconstruction
  4. 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)