MIT Number Theory Seminar

Sam Schiavone (MIT)

Title: "On algebras of low rank"

Abstract: In this talk I will discuss algebras of low rank. The main goal
is to study the moduli space of rank 3 algebras, which we will do using
explicit equations. Our investigation leads to a generalization of a
theorem of Levin that shows that rank 3 algebras over an integral domain
occur in essentially two types. We extend this result to rank 3 algebras
over a commutative ring, and then to sheaves of rank 3 algebras over a
scheme.