Topology, Algebraic Geometry, and Dynamics Seminar (TADS): The fundamental theorem of algebra for varieties

Speaker: Neil Epstein, GMU

Title: The fundamental theorem of algebra for varieties

Abstract: The Fundamental Theorem of Algebra can be thought of as a statement about the real numbers as a space, considered as an algebraic set over the real numbers as a field. In this talk, I introduce what it means for an algebraic set or affine variety over a field to be fundamental, in a way that encompasses the usual fundamental theorem of algebra. I also introduce the related concept of *local* fundamentality and develop its behavior. On the algebraic side, I introduce the notions of locally, geometrically, and generically unit-additive rings, thus complementing unit-additivity as previously defined by myself and Jay Shapiro, and extend some theorems to these contexts. I show that an affine variety is (locally) fundamental if and only if its coordinate ring is (locally) unit-additive.

Date/Time: April 11, 1:30pm-2:30pm

Location: Exploratory Hall, Room 4208