Department of Mathematics,
University of California San Diego
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Math 211A: Seminar in Algebra
Eric Zhang
University of Washington
Separable simplicial algebras
Abstract:
We study the notion of separability for simplicial algebras over commutative simplicial rings. We develop basic tools such as simplicial centralizers and enriched separable functors. We show that the two natural notions of Azumaya algebra—central-separable and Morita-theoretic—coincide in the simplicial setting. As applications, we prove a simplicial version of the Auslander–Goldman theorem and show that the Brauer group of a commutative simplicial ring is isomorphic to the Brauer group of its degree-zero component. This talk is based on joint work with Xuan Huang, Garcia Sun, and James Zhang.
Host: Lucas Buzaglo
October 12, 2026
3:00 PM
APM 7321
Research Areas
Algebra****************************
