# Piotr Pstrągowski: Chromatic homotopy is algebraic when p > n^2+n+1

**Time: **
Thu 2019-11-14 10.15 - 12.00

**Lecturer: **
Piotr Pstrągowski, Stockholms universitet

**Location: ** Kräftriket, house 6, room 306 (Cramér-rum)

### Abstract

In chromatic homotopy theory, one stratifies the stable homotopy category by fixing a prime and looking at the \(E(n)\)-local parts, which informally see "information up to height \(n\)". As the height grows, these categories become increasingly intricate and converge to the p-local homotopy theory in a precise sense. On the other hand, it has been observed that when the prime is large relative to the height, then the \(E(n)\)-local category simplifies considerably. In this talk, I will show that when \(p > n^2+n+1\), the homotopy category of \(E(n)\)-local spectra is equivalent to a certain derived category of quasi-coherent sheaves, giving a precise sense in which chromatic homotopy theory is algebraic at large primes. I will then discuss application to chromatic Picard groups and algebraic K-theory.