Back to Commutative Algebra Seminar: Spring 2023
Commutative Algebra Seminar
Date: Friday, Apr 21, 2023
Time: 2:00PM - 3:00PM
Location: LCB 222
Keller VandeBogert
Notre Dame
Title |
The Total Rank Conjecture in Characteristic 2 |
Abstract |
The total rank conjecture is a coarser version of the Buchsbaum-Eisenbud-Horrocks conjecture which, loosely stated, predicts that modules with large annihilators must also have “large” syzygies. In 2017, Walker proved that the total rank conjecture holds over rings of odd characteristic, using techniques that heavily relied on the invertibility of 2. In this talk, I will talk about joint work with Mark Walker where we settle the total rank conjecture for rings of characteristic 2. The techniques used are very specialized to the characteristic 2 case, and imply an even stronger result showing that the counterexamples to the generalized total rank conjecture in odd characteristic constructed by Iyengar-Walker are not possible in characteristic 2. |
Commutative Algebra