Nilpotence and descent in equivariant stable homotopy theory

Nilpotence in Stable Homotopy Theory

This talk covers most of section 4 in the Mathew-Naumann-Noel paper [MNN15]. We first discuss nilpotence in an arbitrary symmetric monoidal stable ∞-category. We then discuss the historical origins of nilpotence in the stable homotopy category, namely the Ravenel conjectures and the Nilpotence theorem proved by Devinatz-Hopkins-Smith.

Nilpotence and Periodicity in Stable Homotopy Theory

Contents Preface xi Introduction xiii 1 The main theorems 1 1.

Equivariant stable homotopy theory

We will study equivariant homotopy theory for G a finite group (although this often easily generalizes to compact Lie groups). The general idea is that if we have two G-spaces X and Y , we’d like to study homotopy classes of equivariant maps between them: [X,Y ] = Map(X,Y )/htpy, where Map(X,Y ) = {f : X → Y |f(gx) = gf(x) for all g ∈ G}. In classical homotopy theory (i.e. when G is the trivial...

Nilpotence and Stable Homotopy Theory II

Spectral Sequences in (equivariant) Stable Homotopy Theory

1. The homotopy fixed-point spectral sequence: 5/15/17 Today, Richard spoke about the homotopy fixed-point spectral sequence in equivariant stable homotopy theory. We’ll start with the Bousfield-Kan spectral sequence (BKSS). One good reference for this is Guillou’s notes [4], and Hans Baues [2] set it up in a general model category. We’ll work in sSet, so that everything is connective. Consider...