Between Characteristic Zero and Characteristic p. Lecture 2: Representation Theory in Intermediate Characteristic

In algebra and algebraic geometry, there is often a stark difference between the behavior of fields of characteristic zero (such as the complex numbers) and fields of characteristic $p$ (such as finite fields). For example, the equation $x^p = 1$ has $p$ distinct solutions over the field of complex numbers, but only one solution over any field of characteristic p. In this series talks, I'll introduce the subject of $K(n)$-local homotopy theory, which in some sense interpolates between characteristic zero and characteristic $p$, and describe the curious behavior of roots of unity in this intermediate regime.

Speaker: Jacob Lurie, Harvard