Math 746, Fall 2024, Professor Kustin

• CLASS NOTES, 2024.
  
  
• In class on Monday December 2, we covered pages 78-80 from the class notes.
  
  
• Up to date as of December 4, 2024, 11:27 AM.
  
  

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  Some Possible Projects

• Some Possible Projects, Fall 2024.

  References Related to the Possible Projects

• Avramov, Infinite free resolutions.
• Barwick, Dissertation.
• Buchsbaum and Eisenbud, What makes a complex exact?
• Cohen, Commutative rings with restricted minimum condition.
• Conrad, Dedekind Domains.
• Cuong, Dao, Eisenbud, Kobayashi, Polini, and Ulrich, Syzygies Of The Residue Field Over Golod Rings.
• Distler, Donagi, and Donagi, On Generalized Pfaffians.
• Hochster, The structure theory of complete local rings.
• Kustin, Pfaffian identities, with applications to free resolutions, DG-algebras, and algebras with straightening law.
• Kustin, Syzygies.
• Nguyen and Veliche, A truncated minimal free resolution of the residue field.
• Pollitz and Sega, Relations between Poincare series for quasi-complete intersection homomorphisms.
• Schnibben, Local Rings and Golod Homomorphisms.

Announcements

• Syllabus, Fall 2024.
  
  
• Course Announcement: Commutative Algebra Course, Fall 2024.
  
  
• A link to the website I used when I taught this course in Fall 2018.
  
  
• A link to the website I used when I taught this course in Fall 2013.
  
  
• Some of my favorite references are:
  • Atiyah and Macdonald, "Introduction to Commutative Algebra".
  • Bruns and Herzog, "Cohen-Macaulay rings".
  • Eisenbud, "Commutative algebra with a view toward Algebraic Geometry".
  • Matsumura, "Commutative Algebra".
  • Matsumura, "Commutative Ring Theory".
  
  
• My favorite software is Macaulay2. Here is a small Macaulay2 session where I calculated the primary decomposition of an ideal. I used a session like this as I prepared the lecture (in 2013) on primary decomposition. All of the commands I used are explained on-line. I find the Macaulay2 Table of Contents to be very helpful.
  
  
• Many people post their pre-prints on the arXiv. Here is a short fascinating paper that appeared on the arXiv on Tuesday, August 27, 2024. Syzygies-Of-The-Residue-Field-Over-Golod-Rings.pdf

Old Announcements

• In class on Wednesday August 21, we covered pages 8-10 from the class notes.
• In class on Monday August 26, we covered pages 10-13 from the class notes.
• In class on Wednesday August 28, we covered pages 13-16 from the class notes.
• In class on Wednesday September 4, we covered pages 16-19 from the class notes.
• In class on Wednesday September 18, we covered pages 25-28 from the class notes.
• In class on Monday September 23, we covered pages 35-37 from the class notes.
• In class on Wednesday September 25, we covered pages 37-40 from the class notes.
• In class on Wednesday October 2, we finished the proof of the Theorem about primary decomposition and started considering Krull dimension.
• In class on Monday October 7, we covered pages 44-47 from the class notes.
• In class on Wednesday October 9, we covered pages 47-49 from the class notes.
• In class on Monday October 14, we covered pages 53-55 from the class notes.
• In class on Wednesday October 16, we covered pages 53-55 from the class notes.
• In class on Monday October 21, we covered pages 55-57 from the class notes.
• In class on Monday November 18, we covered pages 72-73 from the class notes.
• In class on Wednesday November 20, we covered pages 73-78 from the class notes.