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Presented By: Commutative Algebra Seminar - Department of Mathematics

Commutative Algebra Seminar: The Total Rank Conjecture in Characteristic Two

Keller VandeBogert (Notre Dame)

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 speak on joint work with Walker where we settle (and generalize) the total rank conjecture over k-algebras of arbitrary characteristic. Our techniques take advantage of the classical Dold-Kan correspondence and allow us to prove an even stronger version of the total rank conjecture when the field k has characteristic 2.

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