Ramification Theory

• Topics: Kahler differentials, ramification for maps of noetherian rings following Auslander-Buchsbaum and Nagata, Differents, Applications to invariant theory.
• Pre-requisites: localisation, associated primes and primary decomposition, integral extensions, Noether normalization lemma, nullstellensatz dimension theorem for noetherian local rings, completion, homological methods in commutative algebra (Ext, Tor, flatness, regular local rings, etc.)
• References :
  • Auslander and Buchsbaum, Ramification theory of noetherian rings American Journal of Mathematics (1959)
  • Benson, Polynomial invariants of finite groups, Cambridge Univ Press.
  • Berger, Uber verschiedene Differentenbegriffe, Sitzungsberichte Heidelberger Akademie der Wissenschaften, Math.-Nat. Kl. 1960/61
  • Eisenbud, Commutative algebra with a view towards algebraic geometry, Springer.
  • Kunz, Kahler differentials, Springer
  • Matsumura, Commutative algebra, Benjamin/Cummings, 1980
  • Matsumura, Commutative ring theory, Cambridge Univ Press.
  • Nagata, Local rings, Interscience.
  • Scheja and Storch, Lokale Verzweigungstheorie, notes from Mathematics Institute of University of Freiburg, 1973
• All the information regarding this course will be posted on Moodle. You can directly access the course page at http://moodle.cmi.ac.in/course/view.php?id=1069 . Otherwise, look for `Ramification Theory' under `Mathematics / Aug-Nov 2025'.
• This is only the preliminary information. For the document containing course policies, log in to the Moodle site for the course and look for `Course Policies'.