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Algebra Seminar

Friday, March 18, 2022 - 3:30pm

Danny Krashen

University of Pennsylvania


University of Pennsylvania


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Division algebras, and more generally central simple algebras have played an important role in understanding field arithmetic. In 1944, Châtelet made an important observation, giving a correspondence between central simple algebras and a certain class of algebraic varieties, which became known as Severi-Brauer varieties. This observation has allowed for structural questions about central simple algebras to be recast as geometric problems about Severi-Brauer varieties, and vise-versa. In this talk, I'll describe some extensions of work of Karpenko along these lines, which relates the writing a central simple algebra as a tensor product of smaller algebras to questions about the Chow group of the corresponding Severi-Brauer variety.