Back to Commutative Algebra Seminar: Fall 2019
Commutative Algebra Seminar
Date: Friday, Nov 22, 2019
Time: 2:30PM - 3:20PM
Location: LCB 225
Zhan Jiang
University of Michigan
Title |
Closure operations on complete local rings of mixed characteristic |
Abstract |
Closure operations are important tools in commutative algebra. The most well-known closure operation is tight closure introduced by Hochster and Huneke, which turns out to be very powerful and fruitful. Other examples are epf and r1f closures defined by Heitmann for rings of mixed characteristics. Dietz and R.G. axiomatized some nice properties of tight closure and its relation to big Cohen-Macaulay algebras/modules. In this talk, I will introduce their axioms and define a new closure operation called “weak epf closure” in mixed characteristic. This closure operation satisfies all axioms mentioned above, which suggests that it may be a good analog of tight closure. Other related results and open questions will be discussed. |
Commutative Algebra