All Questions
12
questions
2
votes
0
answers
128
views
A basic computation with spectra
Let $\mathbb{E}=\big(E_n, \sigma_n\colon T\wedge E_n\to E_{n+1}\big)_{n\in\mathbb{N}}$ be a $T$-spectrum, either in the topological setting (with $T=S^1$) or in the algebraic setting (with $T=\mathbb{...
- 2,811
4
votes
1
answer
179
views
(Algebraic) cobordism and the rank function
I write the question for algebraic cobordism but I have the analogue question for classic cobordism.
The spectrum representing algebraic cobordism
$$
\mathbf{MGL}=(*, \mathrm{Th}(1) , \ldots , \mathrm{...
- 2,811
4
votes
0
answers
195
views
Direct image and infinite suspension
I have a basic doubt regarding infinite suspension functor and the direct image. I write it for schemes but I guess it works the same for the topological setting so I welcome answers also from the ...
- 2,811
3
votes
1
answer
290
views
Infinite loop space of ring spectra: the cup product
I have a basic question on homotopy theory, and I would welcome answers or references both from the classic and the motivic context of homotopy theory.
Let $\mathbb{E}=(E_n)_{n\in \mathbb{N}}$ be an ...
- 2,811
4
votes
0
answers
104
views
Unstable and stable looping and delooping
I have some basic questions on the relation of looping and delooping in the stable and unstable homotopy categories. I state them it in the motivic setting, but if somebody has an answer for an ...
- 2,811
3
votes
1
answer
293
views
Basic questions on spectra
I have a basic question on Voevodsky's stable homotopy category of spectra $\mathbf{SH}(S)$, where $S$ is a finite dimensional noetherian scheme.
Let $E$ be an $\Omega$-spectrum and $\varphi \colon ...
- 2,811
4
votes
0
answers
766
views
Access to a classic reference of Dold-Puppe
There is an old reference that I am unable tofind. It is Dold-Puppe´s communication at a conference. More concretely, it is cited as:
A. Dold, D. Puppe: Duality, trace and transfer. Proceedings of the ...
- 2,811
10
votes
1
answer
518
views
When is the Thom spectrum of a virtual vector bundle effective?
Remark: My question is valid in the classic setting of the stable homotopy category of spectra of CW-complexes. An answer on that setting will also be valid.
Denote as $SH(X)$ Voevodsky's stable ...
- 2,811
16
votes
1
answer
814
views
Representability of Weil Cohomology Theories in Stable Motivic Homotopy Theory
My understanding is that one purpose of stable motivic homotopy theory is to emulate classical stable homotopy theory. In particular, we would like Weil cohomology theories to be representable by ...
- 161
3
votes
1
answer
279
views
Triangulated structure on $\mathbf{SH}(S)$: $\mathbb{P}^1$-suspension versus classical suspension
I am studying the construction of the motivic stable homotopy category of schemes $\mathbf{SH}(S)$ following Riou's paper Categorie homotopiquement stable d'un site suspendu avec intervalle (click to ...
- 2,811
7
votes
2
answers
398
views
Properness of the category of modules over a spectrum (that represents algebraic cobordism or motivic cohomology)
The abstract form of the question: let $C$ be a closed proper stable model category, $R$ is a ring object in it. Which conditions ensure that the category $R-mod$ is also proper?
Since weak ...
- 16.7k
9
votes
1
answer
590
views
Is the injective model structure on symmetric spectra Bousfield localizable?
I am interested in injective model structures on both symmetric spectra as exposed in Hovey/Shipley/Smith and motivic symmetric spectra as in Jardine's article. Both authors take a model structure on ...
- 12.1k