# Tagged Questions

**5**

votes

**1**answer

233 views

### Detection of stable homotopy by K-theory spectra

This is primarily a reference request. Does anyone know of any writing about algebraic K-theory spectra picking up elements in the stable homotopy groups of spheres in their Hurewicz image coming from ...

**4**

votes

**0**answers

165 views

### Which ring spectra have some kind of exponential map turning addition into multiplication?

This accepted answer to the question about $BU_\otimes$ made me recall that I want to read about this general phenomenon for a long time.
What will follow is sort of vernacular but whether it can be ...

**2**

votes

**0**answers

153 views

### Quillen functors and stable model categories

Are there any books or papers where I can find some general statements and methods for working with Quillen functors that are not equivalences (and not localizations)? In particular, I would like to ...

**2**

votes

**1**answer

186 views

### Compact MU or BP Modules

Is there a classification of the compact MU or BP modules in any category of spectra? Can the periodicity theorem be finagled to give a MU-module structure on finite spectra?

**3**

votes

**1**answer

125 views

### Interesting examples of a 4-torsion X in a triangulated category such that $2 End(X/2X)\neq 0$?

It is well-known that for the sphere spectrum $S$ in the ('topological') stable homotopy category the object $S/2S$ i.e. the cone of $S\stackrel{\times 2}{\to}S$, is not $2$-torsion.
So I wonder ...

**7**

votes

**1**answer

295 views

### The vanishing of $MGL^{2n+i,n}(X)$; do spectra of smooth projective varieties generate $SH_{l}$?

I have two questions related to the stable motivic homotopy categories of Morel-Voevodsky. The first is probably simple; I wonder what is known on the second one.
For the algebraic cobordism theory ...

**2**

votes

**3**answers

428 views

### Fracture Squares of Bousfield Localizations of Spectra

Suppose I have a spectrum $X$ and two homology theories $E$ and $F$. If I look at the Bousfield localizations, $L_E$, $L_F$, $L_{E\vee F}$ and $L_{E\wedge F}$, do I have a homotopy pullback square ...

**3**

votes

**2**answers

349 views

### Reference request: Spec A_* is the automorphism group of the additive formal group law

Dear all,
I'm seeking a reference for a claim made in lecture 8 of Jacob Lurie's chromatic homotopy theory notes (http://www.math.harvard.edu/~lurie/252xnotes/Lecture8.pdf). More particularly, ...

**23**

votes

**1**answer

718 views

### Early stabilization in the homotopy groups of spheres

Thanks to Freudenthal we know that $\pi_{n+k}(S^n)$ is independent of $n$ as soon as $n \ge k+2$. However, I was looking at the table on Wikipedia of some of the homotopy groups of spheres and noticed ...

**7**

votes

**1**answer

743 views

### A heart for stable equivariant homotopy theory

Let $G$ be a finite group. I wonder whether the following statement is true, known and written down:
There is a t-structure on the stable $G$-equivariant homotopy category such that the associated ...

**3**

votes

**3**answers

337 views

### Are there universe-indexed spectra over simplicial sets?

In "Rings, Modules, and Algebras in Stable Homotopy Theory" Elmendorf, Kriz, Mandell and May introduce a notation of spectra indexed over an universe $\mathcal{U}$ as a collection of pointed ...